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COURTIS  STANDARD 

PRACTICE  TESTS 

IN  ARITHMETIC 


TEACHER'S  MANUAL 

For  use  with  the  Card-Cabinet  Edition 
BY 

S.  A.  COURTIS 

Supervisor  of  Educational  Research,  Detroit  Public  Schools. 


Contains  full  instructions  for  the  proper 
use  of  the  Standard  Practice  Tests  in 
Arithmetic,  together  with  sample  graphs 
and  records  and  suggestions  for  the  diag- 
nosis and  remedy  of  the  difficulties  of  in- 
dividual children,  by  means  of  which 
alone  it  is  possible  to  effect  any  radical 
improvement  in  the  efficiency  of  teaching. 


WORLD  BOOK    COMPANY 

YONKERS-ON-HUDSON,  NEW  YORK 


STANDARD     PRACTICE    TESTS 


Personal  Note  to  Teachers: 

The  Courtis  Standard  Practice  Tests  in  Arithmetic  were  , 
designed  to  decrease  the  amount  of  a  teacher's  routine  drudgery  j 
and  to  improve  the  efficiency  of  his  teaching.     Measurement  | 
proves  that  when  the  tests  are  rightly  used  both  objects  are  ac- 
comphshed.    Measurement  also  proves  that  the  degree  of  suc- 
cess attained  depends  upon  how  far  the  teacher  comprehends 
the  purpose  of  this  new  tool,  and  uses  the  opportunities  it  pro- 
vides for  adjusting  the  drill  work  to  the  needs  of  the  individual 
children.    Will  you  not,  therefore,  study  the  instructions  care- 
fully until  you  understand  the  essential  features  of  the  system, 
then  make  such  adjustment  of  the  general  method  to  your  local 
conditions  as  will  enable  you  to 

a.  Measure  your  class  to  determine  the  initial  ability  of  its 
members. 

(See  pages  6,  7-11) 

b.  Eliminate  from  the  drill  class  those  who  have  (or  reach) 
standard  ability. 

(See  pages  6,  11-13) 

c.  Give  to  each  of  the  other  members  drill  upon  those  les- 
sons where  drill  is  needed. 

(See  pages  6,  13) 

d.  Permit  each  individual  to  practice  in  his  own  way  and 
to  grow  at  his  own  rate. 

(See  pages  6,  20-27) 

e.  Give  exactly  the  assistance  needed  to  each  child  that 
fails. 

(See  pages  27-44) 

f.  Measure  the  efficiency  of  your  teaching. 

(See  page  22) 

If  you  will  do  this  faithfully  and  intelligently,  the  efficiency 
of  your  teaching  of  the  four  operations  with  whole  numbers  will 
rise  from  the  conventional  5%  to  10%  to  from  60%  to  75%. 

Copyright,  1914,  191 5,  1916,  by   World  Book  Company.   Yonkers-on-Hudson,  New   York. 
'•       .        CSPTA^TM:Ca   Bd-2 


TEACHER'S    MANUAL 


Ten  Essential  Points 

1.  The  purpose  of  the  Practice  Tests  is  to  develop  ability 
that  will  transfer  to  regular  arithmetic  work,  and  to  all  situa- 
tions in  which  computations  are  used ;  not  to  give  a  few  children 
a  chance  to  show  how  rapidly  they  can  finish  the  series  of 
lessons. 

2.  Lack  of  ability  to  "cipher"  will  prove  a  handicap  in 
the  life  of  any  man  or  woman.  On  the  other  hand,  once 
standard  degrees  of  ability  have  been  attained,  further  drill 
is  a  waste  of  time  and  effort.  Children  of  standard  ability 
should  be  set  at  more  profitable  work. 

3.  Ten  minutes  a  day,  day  after  day,  spent  in  intense, 
purposeful,  snappy  practice,  has  proved  adequate  to  develop 
proper  habits  of  speed  and  accuracy.     Why  use  more? 

4.  Skill  cannot  be  developed  in  growing  children  by  in- 
struction, or  by  any  other  form  of  personal  exertion  on  the 
part  of  the  teacher.  Consequently  the  teachers  who  best 
inspire  their  classes  to  voluntary  effort  will  secure  the  best 
returns. 

5.  Mere  repetition  does  not  develop  skill;  it  is  repetition 
accompanied  by  the  conscious  desire  to  improve  that  brings 
results.  Mark  for  growth^  not  for  the  number  of  lessons 
completed. 

6.  Remember  always  that  "nothing  succeeds  like  success." 
It  is  easy  to  get  a  child  to  try  once,  but  he  will  not  keep  on 


Q*yA  i  ^ej 


4 STANDARD     PRACTICE    TESTS 

trying  unless  his  efforts  bring  success.  The  Practice  Tests 
will  automatically  set  for  each  child  each  day  a  task  within  his 
reach.  If  you  reward  growth  in  proportion  to  effort,  the 
children  will  do  the  rest. 

7.  There  has  always  been  some  cheating  in  school  work, 
and  some  children  will  always  cheat.  The  best  safeguard 
against  cheating  is  not  the  repressive  vigilance  of  authority,  but 
the  development  of  ideals  of  honesty  and  self-mastery. 

8.  The  surest  sign  of  faulty  use  of  the  Practice  Tests  is 
the  speed  that  is  due  to  excessive  effort  and  nervous  strain. 
The  speed  that  is  desired  is  the  perfection  of  execution  pro- 
duced by  thoroughness  of  preparation.  The  speed  that  is 
merely  hurry  makes  for  exhaustion.  Do  not  force  speed. 
Inspire  conscientious  practice  and  the  question  of  speed  will 
take  care  of  itself. 

9.  Under  no  circumstances  forget  that  when  a  child  fails, 
there  is  a  reason,  and  that  only  as  you  discover  the  true  reason 
will  you  be  able  to  render  real  assistance.  Neither  age,  experi- 
ence, training,  nor  "pull"  will  make  a  wrong  diagnosis  effec- 
tive. It  pays  to  take  the  time  necessary  to  determine  the 
causes  of  the  difficulties  of  individuals,  because  then,  and  then 
only,  can  you  apply  the  proper  remedy. 

10.  Through  appeals  to  basic  instincts,  drill  work  with 
the  Practice  Tests  becomes  so  interesting  and  enjoyable  that 
it  takes  on  the  nature  of  play.  This  in  no  way  decreases  the 
value  of  the  results  secured,  however.  See  that  the  children 
look  forward  to  the  drill  period  as  to  play  time,  and  have  a 
little  human  interest  yourself  in  the  records  made. 


TEACHER'S     MANUAL 


Section  I 
General  Description 

Each  child  should  be  supplied  with  a  Student's  Record  and  Practice  Pad 
and  the  teacher  with  a  cabinet  of  lesson  cards  and  a  Teacher's  Manual.  Each 
lesson  card  in  the  cabinet  consists  of  a  number  of  examples  of  one  type,  the  types 
being  so  chosen  that  the  range  is  from  the  simplest  examples  to  the  most  difficult 
a  child  in  the  grades  is  called  upon  to  solve.  Further,  the  mastery  of  the  examples 
on  each  card  insures  the  mastery  of  some  one  of  the  many  component  elements 
that  enter  into  skill  in  the  four  operations.  In  addition,  for  instance,  one  of 
the  early  lessons  is  designed  to  [teach  the  combinations,  another  the  bridging  of 
the  tens,  another  carrying,  another  control  of  the  attention  span.  Four  of 
the  cards  (Lessons  45,  46,  47,  and  48)  are  study  cards  for  the  use  of  children 
who  have  trouble  in  learning  the  combinations.  Four  other  cards  (Lessons 
13,  30,  31,  and  44)  are  test  cards  to  be  used  in  determining  what  practice  a 
child  needs,  and  in  measuring  the  efficiency  of  the  child's  efforts.  These  eight 
cards,  strictly  speaking,  are  not  practice  lessons,  although  their  use  is  essen- 
tial to  the  success  of  the  plan.  The  lessons  are  issued  in  two  editions.  Form 
A  and  Form  B.  The  examples  in  these  two  forms  differ,  but  the  two  forms 
are  equal  in  the  number  and  difficulty  of  the  examples  in  each  lesson.  In 
filling  an  order,  equal  quantities  of  Form  A  and  Form  B  are  supplied;  the  two 
should  be  equally  distributed  in  each  class.  It  makes  no  difference  whether 
a  child  begins  to  work  on  Form  A  or  Form  B.  The  corresponding  lessons 
of  either  form  serve  as  a  test  for  the  study  and  practice  put  upon  the  other. 
No  one  lesson  in  the  same  grade  should  take  any  longer  to  complete  than 
any  other  lesson. 

The  remaining  forty  cards  are  practice  lessons  and  are  used  as  follows: 

A  lesson  card,  practice  side  up,  is  placed  under  the  topmost  tissue-paper 
sheet  of  the  Student's  Practice  Pad.  The  child  sees  the  examples  through 
the  paper  but  does  his  work  directly  upon  the  tissue-paper  sheet.  The  num- 
ber of  examples  in  each  lesson  has  been  so  chosen  with  respect  to  the  diffi- 
culty of  the  examples  that  all  the  lessons  require  the  same  working  time. 
That  is,  an  eighth-grade  child  of  standard  ability,  for  instance,  will  require 
three  minutes  to  finish  each  and  every  lesson.^ 

At  the  end  of  the  practice  period,  the  card  is  taken  out,  turned  over 
that  the  answer  side  is  uppermost,  and  again  placed  under  the  tissue- 
paper  sheet.  It  is  then  easy  for  the  child  to  compare  his  answers  with  the 
true  answers  and  find  his  own  mistakes.  The  perforated  tissue  sheets  are 
now  torn  out,  but  only  the  papers  the  children  judge  to  he  perfect  are  handed 
in^,  so  that  the  teacher  is  relieved  of  much  drudgery  of  correction  of  papers. 
The  lesson  cards  are  printed  on  strong  cardboard  and  may  be  used  again 
and  again,  and  year  after  year.  It  is  the  supply  of  tissue-paper  sheets  that 
is  renewed  each  year. 

^Except  those  marked  "Double  Time,"  which  require  six  minutes. 


6  STANDARD     PRACTICE     TESTS 

The  scores  made  each  day  are  recorded  by  the  child  in  the  Student's  Record, 
and  graphs  drawn  that  the  child  may  see  the  effect  of  his  own  practice.  In 
other  words,  the  children  take  care  of  their  own  progress  in  every  possible 
way,  that  the  teacher  may .  be  relieved  of  the  mere  mechanical  details  of 
preparation  and  marking,  in  order  that  he  may  give  his  time  to  the  actual 
teaching  of  children. 

Program 

At  the  beginning  of  the  term,  the  first  activity  is  measurement.  The 
teacher  gives  Lesson  13  (Test  A)  to  determine  which  children  need  drill 
on  Lessons  1-12.  Those  who  have  perfect  scores  are  excused  from  drill 
work  until  the  rest  of  the  class  has  completed  these  lessons.  Their  drill 
time  is  spent  upon  other  work. 

The  next  day  the  remaining  children  take  Lesson  1.  The  third  day 
those  who  are  successful  take  Lesson  2,  and  sc  on.  But  those  who  failed 
on  Lesson  1  spend  the  third  drill  period  in  practicing  the  examples  in  the 
lesson,  and  the  following  day  try  the  lesson  again,  to  test  the  effectiveness 
of  their  practice.  Only  when  Lesson  1  has  been  completed  successfully  do 
they  go  on  to  Lesson  2. 

In  this  way  each  child  masters  the  simple  work  before  attempting  the 
more  complex;  each  child  practices  only  on  the  type  of  example  in  which 
he  falls  below  the  standard,  and  each  child  progresses'  as  fast  or  as  slowly 
as  his  native  powers  and  personal  efforts  allow.  At  the  end  of  two  months 
each  child  in  a  class  of  40  may  be  working  on  a  different  lesson. 

To  a  teacher  reading  the  foregoing  description  for  the  first  time,  it 
may  seem,  that  it  would  be  very  confusing  to  have  children  working  on 
different  lessons  and  progressing  at  different  rates.  It  must  be  remembered, 
however,  that  as  far  as  the  teacher  is  concerned  his  work  is  the  same 
whether  the  child  is  on  Lesson  1  or  on  Lesson  40,  and  that  at  the  start 
(the  most  confusing  time)  all  the  children  work  on  the  same  lesson.  By 
the  time  the  number  of  lessons  in  use  reaches  four  or  five,  the  system  will 
be  running  smoothly  and  will  give  no  trouble. 

There  are  two  important  reasons'  why  eve.ry  teacher  should  be  willing 
to  make  whatever  effort  may  be  necessary  to  adopt  this  new  form  of  class- 
room procedure.  The  first  one  is  that  experimental  psychology  has  proved 
that  children  differ  enormously  in  their  natural  powers  and  rates  of  growth, 
so  that  only  that  teacher  can  be  efficient  who  adapts  school  work  to  the 
needs  of  each  individual  child.  No  teacher,  by  mere  intuition  alone,  can 
make  such  adjustments  for  fifty  children,  while  the  system  described  above 
will  do  it  automatically.  Once  you  have  made  the  system  your  own,  you  will 
get  better  results  than  ever  before  and  with  less  effort. 

The  second  reason  is  that  the  system  itself  has  been  a  gradual  evolu- 
tion. It  is  based  primarily  upon  a  careful,  scientific  measurement  of  the 
relative  effect  of  the  various  factors  which  condition  teaching,  and  the 
original   plan  has   been   modified   by  the    contributions   of   many   successful 


TEACHER'S     MANUAL 


teachers.  Each  device  has  been  adopted  in  response  to  a  real  need.  The 
system  as  a  whole  has  proved  practical  in  the  hands  of  a  large  number  of 
teachers  and  is  rapidly  being  extended  to  other  subjects.  You  cannot  afford, 
professionally,  not  to  master  this  new  and  efficient  tool. 

Section  II 
Detailed  Instructions  for  Each  Day  of  the  First  Two  Weeks 

Do  not  begin  the  Practice  Test  work  until  the  second  week  of  school, 
or  until  the  organization  of  your  class  is  completed,  so  that  you  have  some 
knowledge  of  the  personal  characteristics  of  the  children  in  it. 

Monday 
Give  to  each  child  a  card  of  Lesson  1  and  a  Student's  Record 
and  Practice  Pad.^  Show  them  how  to  put  it  in  their  practice  pads 
under  the  topmost  tissue  sheet,  practice  side  up,  so  that  the  ex- 
amples may  be  seen  through  the  paper.  Explain  the  necessity  for 
lifting  the  tissue-paper  sheet  well  up  from  the  rest  of  the  pad,  and 
pushing  the  card  as  far  up  into  the  stub  as  possible  so  that  it  will 
be  held  firmly  in  place  and  not  slip.  Have  the  children  read  aloud 
the  instructions  for  starting  and  stopping  as  given  in  the  Student's 
Record,  page  3.  Go  through  the  motions  once  or  twice  until  you 
are  sure  every  child  understands.  Then  let  them  w^ork  on  Lesson 
1  for  a  half-minute  interval,  and  score  their  papers,  following  the 
instructions. 

This,  of  course,  is  mere  practice,  to  make  them  familiar  with  the  general 
procedure. 

Explain  that  the  first  real  work  will  be  to  find  out  which  children 
need  the  drill.  Collect  all  the  cards  of  Lesson  1.  Distribute  the 
cards  of  Lesson  13  and  have  the  children  put  them  in  position  in 
the  practice  pads  ready  for  work.  Warn  the  children  that  to  study 
a  card  before  the  proper  time  is  cheating.  Then  put  the  Lesson  1 
cards  back  into  the  cabinet  in  their  proper  place. 

A  little  care  in  returning  cards  to  the  cabinet  will  enable  you 
to  keep  your  material  in  good  order.  Always  put  a  card  after  the 
numbered  separator,  with  the  top  of  the  card  to  the  left,  the  face 
of  the  card  towards  you.  You  will  then  be  able  to  select  Form 
A  or  B  as  need  arises.  Assign  the  task  of  filing  the  returned  cards 
each  day  to  the  children  who  are  excused  from  drill.  It  is  ex- 
cellent practice  in  an  important  form  of  office  work.  Have  all  the 
pads  and  cards  put  away  ready  for  the  work  of  the  next  day. 

Tuesday 

For  the  testing  work,  the  teacher  needs  a  timepiece  showing  seconds. 
A  dollar  watch  having  a  second  hand  does  very  nicely.  A  football  timer 
(price  $2.50  at  any  store   that   sells   sporting   goods)   is  very  much  better,  as 

1  If  the  children  buy  this  material  themselves,  be  sure  that  all  are  supplied  before  you 
begin  explanations. 


Low  sixth 

grade, 

4:}i  minutes 

High  fifth 

grade, 

4^  minutes 

Low  fifth 

grade. 

5}i  minutes 

High  fourth 

grade, 

5}i  minutes 

Low   fourth 

grade, 

634  minutes 

8 STANDARD     PRACTICE     TESTS 

it  starts   from  zero,   and  shows  minutes   and  seconds  of   elapsed  time  more 
clearly  than  a  regular  watch. 

It  is  of  the  utmost  importance  that  the  teacher  use  scientific  care  in 
keeping  exact  time.  H  the  time  interval  varies  from  day  to  day,  the  chil- 
dren's scores  will  vary  for  no  apparent  reason,  and  the  whole  force  of  the 
timing  be  lost. 

Give  the  signal  to  start  just  as  the  second  hand  reaches  the  sixty 
mark,  and  give  the  signal  to  stop  sharply  at  the  end  of  the  interval. 

The  time  to  be  allowed  for  the  various  grades  is  as  follows: 

High    eighth  grade,  3       minutes 

Low   eighth  grade,  Z]/^  minutes 

High  seventh  grade,  3^/2  minutes 

Low  seventli  grade,  3^  minutes 

High  sixth  grade,  4      minutes 

All  lessons  in  any  one  grade  are  to  have  the  same  time  allowance. 

Those  to  whom  these  standards  seem  high  are,  of  course,  at  liberty  to 
change  these  time  allowances  to  suit  their  own  ideas. 

The  standards  above,  however,  have  been  set  after  a  careful  investigation 
of  the  actual  speed  of  work  of  children  in  the  grades,  and  are  believed  to 
represent  the  speeds  at  which  children  can  work  without  strain.  Speed  is 
apparently  fixed  by  the  maturity  of  the  individual,  so  that  there  is  an  op- 
timum speed  for  each  age. 

H  a  teacher  has  several  grades  in  one  room,  he  may  adopt  one  of 
several  methods.  The  best  way  is  probably  to  start  all  the  children 
together,  and  give  each   grade  its  own  signal  to   stop. 

For  instance,  in  a  room  having  both  A  6th  and  B  7th  children,  the  teacher 
should  start  all  together,  and  at  the  end  of  3^  minutes  should  say  "B  7th, 
stop^.  Hands  up.  Score  your  papers,"  and  at  the  end  of  four  minutes,  "A  6th, 
stop.     Hands  up.     Score  your  papers." 

Other  methods  are  to  use  the  time  of  the  youngest  grade,  or  of  the 
largest  grade,  but  either  of  these  methods  means  a  lack  of  adjustment  for 
some  children.  If  this  is  done,  however,  it  is  better  to  have  the  time  too 
long  than  too  short. 

Still  anothet  method  is  to  use  the  time  of  the  oldest  class  for  all,  but 
require  all  other  classes  to  do  but  a  part  of  the  test.  The  following  table 
shows  the  per  cent  of  each  lesson  that  should  be  completed  by  each  grade 
for  each  time  allowance: 


TEACHER'S     MANUAL 


Time 

Grades 

Allowanc 

e, 

8 

7 

6 

5 

4 

Minutes 

H 

L 

H          L 

H 

L 

H 

L 

H 

L 

3      100% 

92% 

85%     80% 

75% 

70% 

63% 

57% 

42% 

38% 

354 

100 

92        87 

81 

76 

68 

62 

56 

52 

3>^ 

100         93 

87 

82 

73 

66 

61 

5Q 

3^ 

100 

94 

88 

79 

71 

65 

60 

4 

100 

94 

84 

76 

69 

64 

414 

100 

89 

81 

74 

68 

m 

100 

90 

82 

76 

534 

100 

91 

84 

5>4 

100 

92 

Q% 

100 

For  instance,  if  a  teacher  used  a  time  allowance  of  four  minutes  with 
his  oldest  class  (High  6th),  for  the  low  sixth  he  would  set  94%  of  the 
examples  in  Lesson  1,  or  68  (72  x  94%)  examples  as  the  number  to  be 
completed.     This  is  a  good  method,  but  a  little  difficult  to  handle. 

The  teacher  should  work  out  and  post  on  the  board  the  number  of 
examples  to  be  completed  by  eaeh  grade  for  each  lesson. 

Work  may  be  done  in  either  pencil  or  ink. 

Probably  ink  is  to  be  preferred,  particularly  in  the  upper  grades,  as 
children  should  learn  to  write  rapidly  and  neatly  with  ink.  Most  commercial 
work  requires  a  permanent  record,  and  is  done  in  ink. 

Having  decided  the  plan  to  be  followed,  give  Lesson  13  to  all, 
following  the  instructions  in  the  Student's  Record. 

The  answers'  to  the  test  cards  are  not  given  on  the  back  of  the  cards 
as  in  the  regular  lessons,  but  are  found  in  the  Teacher's  Manual  on  pages 
54-57.  Note  that  there  are  two  forms  of  Lesson  13,  A  and  B.  Both  sets  of 
answers  will,  of  course,  have  to  be  read. 

Have  the  children  exchange  papers,  and  mark  each  wrong  answer 
with  a  cross  as  you  read  the  correct  answers  from  the  manual. 

In  checking  similar  work  in  business,  it  is  customary  to  read  the  figures 
in  order  without  giving  them  their  place  values.  The  figures  should  be  read 
in  groups  of  three,  with  scarcely  perceptible  pauses  between  tlie  periods. 
Thus  3,456,789  would  not  be  read  three  million,  four  hundred  fifty-six  thou- 
sand, seven  hundred  eighty-nine,  but  three  (pause),  four  five  six  (pause), 
seven  eight  nine.  If  the  answers  are  read  slowly,  the  scoring  of  the  children 
may  be  depended  upon  in  all  but  the  lowest  grades. 

An  answer  Is  to  be  counted  wrong  if  it  is  illegible  because  of  poor 
figures,  or  if  it  has  been  written  over,  or  erased,  or  corrected  in  any  way 
after  the  first  writing,  even  if  the  error  was  discovered  before  the  answers 
were  read.  The  reason  for  this  drastic  rule  is  twofold:  (1)  it  prevents 
cheating,  and  (2)  it  emphasizes  the  need  of  close  attention  and  absolute 
accuracy. 


10 STANDARD     PRACTICE     TESTS 

The  purpose  of  the  Practice  Tests  is  to  develop  habits  of  accuracy  and 
this  cannot  be  done  if  any  form  of  correction  is  tolerated.  Experience  has 
shown  that  absolute  accuracy  in  first-draft,  straight-ahead  work  is  easily 
attainable  by  from  30%  to  50%  of  the  children,  and  that  the  accuracy  of  the 
remaining  children  can  be  brought  to  very  high  levels  if  the  ideal  is  constantly 
kept  in  mind> 

Have  the  children  count  the  number  of  examples  tried,  and  the 
number  right. 

These  results  will  be  called  their  scores.  The  small  figures  written  to 
the  right  and  above  certain  examples  in  the  lessons  save  time  in  counting. 
Teach  the  children  to  go  back  to  the  small  figure  nearest  the  point  where 
they  stopped,  and  count  only  from  that  point  on.^  In  this  way  they  will 
never  have  to  count  riiore  than  four  examples.  In  getting  the  number  right, 
it  is  usually  better  to  count  the  number  wrong  and  subtract  from  the  number 
tried. 

The  scores  from  Test  A  are  to  be  written  in  the  summary  on 
page  5  of  the  Student's  Record.  Have  the  children  point  to  their 
open  records  on  their  desks,  while  you  go  rapidly  up  and  down 
the  aisles  making  sure  each  record  is  in  the  right  place. 

Take  pains  with  the  records  for  the  first  week,  and  you  will  have  no  trouble 
later. 

The  child  should  understand  that  the  keeping  of  a  neat  record  book  is  part 
of  the  work,  that  in  business  and  in  life  they  will  often  have  occasion  to  make 
such  records,  and  that  the  two  things  demanded  are  accuracy  and  neatness. 
Exhibit  sample  record  books  from  time  to  time,  of  the  wor.st  in  the  room  as 
well  as  the  best,  that  the  children  may  have  some  idea  of  what  is  wanted. 
The  record  book  provides  an  opportunity  for  a  kind  of  valuable  training  which 
is  too  often  neglected  by  teachers  of  arithmetic. 

Ask  the  children  who  completed  all  the  examples  in  the  test  to 
stand,  then  ask  of  those  standing,  that  all  who  had  one  or  more 
examples  wrong  sit  down.  Collect  the  perfect  papers.  Then  ask 
those  who  came  within  one  example,  in  either  speed  or  accuracy,  of 
having  perfect  papers,  to  stand.  Collect  these  papers  also.  Finally, 
collect  the  remaining  papers.  Then  ask  how  many  think  they  could 
do  better  if  they  took  the  same  test  again  the  following  day.  Nearly 
all  will  respond.  Promise  to  give  them  another  trial  and  have  the 
pads  put  away. 

Reliability  of  Results 

Every  teacher  should  understand  that  measurement  of  human  ability  is 
the  measurement  of  a  variable  quantity.  The  amount  and  character  of  the 
work  a  person  can  do  in  a  given  time  varies  from  hour  to  hour  and  from 

.   *  Those  who  do  not  accept  the  opinions  given,  should  make  up  regulations  to  fit 
their  own  convictions. 

^That  is,  a  child  who  had  tried  37  examples,  would  go  back  to  35,  then  count, 
36,  37,  instead  of  counting  the  whole  37  examples. 


TEACHER'S     MANUAL 11 

situation  to  situation.  Fortunately,  however,  if  the  conditions  of  testing  are 
kept  constant,  about  half  the  children  will  have  almost  identically  the  same 
scores  on  the  second  day,  and  of  the  remaining  children,  all  but  about  10% 
will  make  the  same  score  within  two  examples  more  or  less.  There  are 
usually,  however,  about  10%  of  the  average  class  whose  scores  will  vary 
widely  from  their  true  abilities.  Two  tests  are,  therefore,  better  than  one, 
particularly  at  the  beginning  of  the  testing  work,  and  it  will  pay  to  repeat 
the  test  the  next  day. 

Teacher's  Scoring 

After  school  or  at  some  convenient  time  go  over  the  papers 
handed  in.  Place  them  over  the  proper  page  in  your  Manual  and 
make  sure  the  children  have  made  no  mistakes  in  scoring.  Enter  the 
scores  in  your  record  on  page  45.  Then  fill  out  a  report  similar  to 
that  on  page  51.  Record  the  number  of  children  who  had  perfect 
papers,  and  the  number  who  missed  but  one  example;  find  what  per 
cent  each  of  these  numbers  is  of  the  total  membership  of  the  class. 
Be  sure  to  date  the  report  and  to  mark  it  "First  Trial." 

Such  report  should  be  carefully  preserved,  as  comparisons  with  later 
tests  will  show  the  efficiency  of  the  teaching. 

Wednesday 

Begin  by  having  the  children  who  on  Tuesday  used  Form  A 
exchange  cards  with  those  who  used  Form  B. 

This  will  tend  to  eliminate  the  effect  of  any  special  "cramming"  that 
may  have  been  done. 

When  all  have  a  different  form  from  the  one  used  Tuesday,  give 
the  test  as  before,  scoring  the  papers  and  entering  the  records,  col- 
lecting the  papers,  and  scoring  and  recording  them  as  before. 

Comparison  of  the  two  results  will  show  how  reliable  the  first  test  was. 

Selection  of  Those  Who  Do  Not  Need  Drill 

Test  A  covers  simple  work  in  the  four  processes.  Children  who  had 
perfect  papers  do  not  need  the  drill  contained  in  the  first  twelve  lessons. 
Moreover,  experiments  have  proved  that  such  children  not  only  do  not  need 
drill,  but  are  likely  to  he  injured  by  it,  so  that  they  would  have  lower  scores 
after  taking  the  drill  lessons. 

Therefore,  put  on  the  board  the  names  of  all  who  had  perfect 
scores  in  both  tests  and  make  it  plain  that  they  are  excused  from  the 
drill  work  in  Lessons  1-12,  and  are  to  spend  the  drill  time  in  study 
upon  such  assignments  as  the  teacher  may  make. 

Try  to  make  the  other  children  understand  that  the  practice  lessons  are 
to  develop  in  them  the  abilities  which  the  perfect  children  already  have.  It 
is  of  vital  importance  that  the  children  understand  that  their  daily  practice 
and  success  in  the  various  drills  are  simply  ^a  means  to  an  end,  and  that  the 
real  measure  of  their  success  will  be  their  scores  when  Test  A  is  reached 
^ts  regular  position  as  Lesson  13. 


12 STANDARD     PRACTICE     TESTS 

Warning.  Lessons  13,  31,  32,  and  44  are  not  practice  lessons  but  tests. 
They  should  not  be  studied  or  practiced  except  under  test  conditions.  With 
children  who  cannot  be  trusted  these  lessons  should  be  collected  at  once  and 
given  out  only  as  tests.  The  teacher  who  is  lax  in  his  care  of  this  point  will 
be  deceived  by  his  results  and  dishonest  in  any  comparisons  he  may  make 
with  the  results  of  other  teachers. 

Alternative  Plans 

The  instructions  above  call  for  the  elimination  of  those  who  had  perfect 
papers  both  days.  Some  teachers  extend  this  to  include  those  who  were 
perfect  either  day,  while  still  others  include  those  who  missed  but  a  single 
example  in  either  speed  or  accuracy.  The  author  advises  the  latter  for 
Grades  4,  5,  and  6,  but  absolute  perfection  both  days  for  Grades  7  and  8.  He 
favors  giving  those  who  missed  but  a  single  example  on  one  of  the  days  a 
third  chance,  counting  the  best  two  out  of  the  three  scores. 

The  course  to  be  followed  from  this  point  on  depends  somewhat  upon 
the  conditions  within  the  class.  If  only  a  few  qualify  for  release  from 
Lessons  1  to  12,  it  is  best  to  begin  the  next  day  with  Lesson  1  and  follow 
the  series  through  in  regular  order  according  to  the  instructions  given  be- 
low. If,  however,  half  of  the  class  or  more  than  half  the  class  are  to  be 
excused,  give  Tests  B  (Lessons  30  and  31)  to  these  children  on  Thursday. 
If,  again,  half  the  class'  have  perfect  papers,  give  Test  C  (Lesson  44) ^  In 
other  words,  children  who  fail  on  Test  A  should  start  on  Lesson  1,  those 
who  succeed  on  Lesson  13  but  fail  on  Test  B  should  start  on  Lesson  14, 
while  those  who  have  perfect  papers  v/ith  the  first  two  tests  but  fail  on 
Test  C  should  start  on  Lesson  31. 

That  is,  the  tests  divide  the  series  of  lessons  into  three  groups,  Lessons' 
1-12,  14-29,  32-43,  each  rnore  difficult  than  the  one, before  it,  so  that  by  means 
of  the  tests  the  teacher  is  able  to  start  each  child  at  the  exact  point  in  the 
series  where  he  needs  drill. 

Children  who  complete  all  the  tests  successfully  do  not  need  the  slightest 
drill  work  in  the  four  operations,  as  they  already  have  more  than  average 
adult  ability  in  these  skills.^  The  author  and  the  publishers  hereby  give 
emphatic  warning  that  the  drill  lessons  are  designed  only  for  children  who 
need  them,  and  that  they  should  not  be  held  responsible  for  the  bad  effects 
and  loss  of  efficiency  sure  to  follow  the  use  of  the  drills  with  children  who 
have  already  attained  the  desired  goal.  Failure  to  determine  the  needs  of 
children  and  to  adjust  individual  work  accordingly  is  one  of  the  greatest 
factors  operating  to  decrease  the  effectiveness  of  almost  all  the  drill  work 
found  in  common  practice. 

The  method  of  handling  the  class  work  also  depends  somewhat  on  the 
conditions  within  the  class,  and  somewhat  upon  the  individual  preference 
of  the  teacher,     ^o^rie  like  to  have  the  class  complete  each  group  of  lessons 

*  Note  that  the  time  allowance  for  Test  C  is  six  minutes. 

''Children  who  complete  all  the  tests  successfully  but  who  are  careless  and 
inaccurate  in  their  regular  arithmetic  work,  should  be  put  back  into  the  drill 
class  until  they  prove  that  they  can  transfer  their  skill  to  the  regular  work. 


TEACHER^S     MANUAL 13 

as  a  unit.  That  is,  no  child  works  on  any  lesson  beyond  13  until  90%  of 
the  class  or  more  have  completed  Lesson  13.  Then  Test  B  is  given  and  the 
second  group  of  lessons  is  carried  through. 

This  method  divides  into  small  groups  the  free  time  of  the  children  who 
are  excused  from  drill  because  of  their  ability.  One  after  another  escapes 
from  the  drill  class  until  all  have  finished  the  first  group  of  lessons,  then  all 
begin  on  the  second  group,  and  so  on. 

Other  teachers  give  Test  A,  then  Test  B  to  those  eliminated  by  Test 
A,  and  Test  C  to  those  eliminated  by  Test  B.  Each  child  then  starts  to 
work  directly  upon  the  lesson  corresponding  to  his  needs. 

Under  this  method,  however,  when  a  child  finishes  the  series  he  has  no 
more  work  to  do,  so  that  if  already  of  standard  ability  he  may  have  one  long 
unbroken  period  without  drill  or  test.  Under  the  first  method,  he  would  at 
least  be  tested  once  every  two  months  and  his  free  time  broken  into  short 
periods. 

The  author  advises  the  first  plan,  and  the  instructions  which  follow  are 
based  upon  it.  When,  however,  most  of  the  class  would  be  excused  from 
drill  to  wait  for  one  or  two  children  to  complete  the  first  group  of  lessons, 
it  is  better  at  once  to  adjust  the  work  of  the  class  to  the  group  of  lessons 
needed  by  the  largest  number  of  children.  Each  teacher  must  decide  for 
himself  the  plan  that  best  suits  the  needs  of  the  class. 

Thursday 

Collect  and  return  to  the  cabinet  the  cards  for  Lesson  13, 
then  supply  all  the  children  not  excused  from  drill  with  the  card 
for  Lesson  1.  Give  the  test  under  standard  conditions,  have  the 
children  score  their  own  papers  and  record  their  scores  in  their 
daily  records. ^ 

Note  that  if  a  child  is  absent,  when  he  returns  he  is  to  record  ''ab" 
(absent)  in  the  place  of  his  scores.  Some  score  is  to  be  recorded  by  each 
child  every  day. 

This  means  that  the  record  book  of  every  child  in   the  room  should  in- 

te  at  any  time  during  the  year  just  how  many  days  the  practice  tests  have 
en  in  use.     If  a  child  enters  late,  his  score  for  his  first  lesson  should  be  writ- 

«i  opposite  the  day  indicated  by  the  books  of  the  rest  of  the  class.  Children 
o  are  excused  from  drill  should  write  *'ex"  for  a  score.  If  the  drill  period 
omitted  for  any  reason,  have  all  the  children  write  ''  om "  for  a  score, 
ese  records  are  necessary  to  compare  the  efficiency  of  teaching  under  differ- 
ent conditions.  It  is  evident  that  it  is  not  right  to  compare  results  in  a  class 
having  practice  every  day  with  one  having  practice  but  three  times  a  week. 
Such  records  will  make  possible  comparisons  on  the  basis  of  loo  days'  prac- 
tice, or  any  other  equal  interval.  They  are  of  the  utmost  importance  in  de- 
termining the  character  of  the  changes  that  need  to  be  made  to  render  the  system 
still  more  efficient. 

When  the  work  of  scoring  and  recording  has  been  completed, 
ask  those  who  had  perfect  papers  to  stand.  Collect  their  cards 
and  papers,  giving  them  in  exchange  cards  for  Lesson  2,  w^hich 


^  On  page  6. 


14  STANDARD     PRACTICE     TESTS 

they  should  put  into  their  pads  in  position  ready  for  work  the  next 
day. 

Have  them  write  *' 2 "  in  the  column  headed  "Lesson"  in 
their  Student's  Record  opposite  Day  2,  then  put  everything  away 
ready  for  the  drill  the  next  day. 

Next  have  the  children  who  missed  on  Lesson  1  stand.  Tell 
them  that  their  scores  show  that  they  need  practice,  and  that  on 
Friday  they  are  to  spend  the  drill  period  in  study  and  practice  on 
Lesson  1,  and  that  the  test  on  Monday  will  show  how  well  they 
study.  Have  these  children  write  "  1  "  opposite  Day  2  in  the  col- 
umn headed  "Lesson,"  and  "pr"  ("practice)  for  their  score,  so 
that  they  will  remember  what  they  are  to  do.  They,  of  course, 
retain  the  cards  for  Lesson  1. 

Teacher's  Scoring 

Go  over  the  perfect  papers  carefully.  At  first  the  children  will  score 
carelessly,  leaving  it  to  you  to  detect  their  mistakes. 

For  the  first  week~or  so,  therefore,  rescore  the  papers  carefully, 
but  keep  a  record  in  your  manual  of  each  child  who  turns  in  a  paper 
in  which  you  find  mistakes.  Such  children,  of  course,  should  study 
Lesson  1  instead  of  trying  Lesson  2  on  Friday.  Put  the  names  of  such 
children  on  the  board  and  for  a  day  or  two  refuse  to  accept  perfect 
papers  from  them  until  their  scoring  has  been  checked  by  other 
children. 

If  you  make  it  a  disgrace  to  hand  in  an  imperfectly  scored  paper,  and 
if  you  keep  a  record  of  the  children  from  whom  such  papers  come,  it  will 
not  be  long  before  you  will  need  to  examine  only  the  papers  from  certain 
children.  After  two  weeks,  the  daily  scoring  and  recording  should  not  take 
more  than  ten  minutes  of  your  time. 

You  should  always  remember  that  mistakes  are  likely  to  happen  with  any 
one.  Even  your  own  scoring  will  not  be  perfect.  It  is  important  only  that 
you  detect  any  cheating  that  may  be  attempted.  It  is  very  foolish  painfully 
and  tediously  to  rescore  each  day  all  the  papers  handed  in.  Such  over-con- 
scientiousness is  just  as  much  to  be  criticized  as  a  failure  to  detect  dishonesty 
m  the  few  children  who  are  sure  to  try  to  deceive  you.  Therefore  use  judg- 
ment in  scoring  and  do  not  wa^te  time  on  such  unprofitable  work  when  it  is 
not  needed. 

In  the  same  way,  use  judgment  in  the  degree  of  perfection  required  for 
perfect  papers.  Do  not  have  the  same  standard  for  all.  If  an  indifferent 
child  is  finally  induced  to  make  a  little  effort,  and  turns  in  a  paper  poor  in 
figures  and  neatness  but  perfect  in  results,  accept  it  and  give  it  the  praise  it 
deserves,  waiting  until  the  habit  of  effort  has  been  well  established  before 
requiring  perfection  in  the  minor  elements.  On  the  other  hand,  set  before 
the  able  children  who  lead  the  class  the  highest  standards  possible.  In  the 
same  way,  the  standards  at  the  end  of  a  term  should  be  higher  than  those  at 
the  beginning. 


TEACHER'S     MANUAL 


15 


Teacher's  Record 

Record  each  day  in  the  record  provided  in  this  Manual  the  papers 
accepted  as  perfect,  by  putting  the  number  of  the  trial  in  the  proper 
space. 

This  will  keep  the  progress  of  the  children  in  such  form  that  you  can 
tell  instantly  the  condition  of  the  class  and  of  individual  children.  A  glance 
at  the  illustration  on  this  page  will  show  the  children  who  are  progress- 
ing rapidly  and  those  making  little  progress.  A  similar  glance  at  the  record 
of  any  one  child  will  tell  the  character  of  his  work.  For  instance,  a  record 
of  15,  8,  and  2  trials  for  Lessons  1,  5,  and  8,  respectively  would  mean  that  a 
child  was  making  very  satisfactory  progress  as  the  number  of  trials  needed  for 
each  additional  lesson  was  steadily  decreasing,  but  a  child  whose  record  was 
five  trials  each  for  these  three  lessons  would  be  doing  little  more  than 
memorizing  the  answers. 

TEACHER'S  RECORD  SHEET 

Name ^  .  .^.-^^C?:?^. 5cAoo/J=l5^rr»?t<r^<r^  Grade  T. . 


Names  of  Children 

Score 

Number  of  Trials  to  complete  successfully  Lesson  1  Score 

test 
A 

1    2 

3 

4 

5   6    7 

8 

9 

10 

11 

12 

test 
A 

1    ZJiyt  J^>ru:t;^ 

2^ 

3  Z 

2 

3 

3/^Z 

/ 

2 

a 

/ 

/ 

29 

a<^7?'^^^xy  /3y..,rur^ 

— 

10 

IS  S 

S  4- 

7 

S 

a  6\4- 

2 

S 

i 

3 

-2 

24- 

3  J^n^  j^JUy<:A. 

S 

5 

— 

3\5\S 

4 

S 

^ 

3 

/2 

The  record  shows  that  John  Smith  had  a  score  of  24  examples  right  (average  of  two 
initial  tests)  at  the  beginning  of  the  work,  that  the  number  of  trials  required  to  complete  a 
lesson  steadily  decreased,  and  that  his  score  in  the  final  test  was  perfect.  May  Brown  has  a 
similar  record  although  her  ability  was  less  at  the  start,  so  that  her  gain  in  the  test  (from  10 
to  24  examples  right)  was  greater  although  she  has  not  yet  overcome  all  her  difficulties  (24 
examples  instead  of  29).  Both  these  records  indicate  excellent  work.  The  record  of  Tom 
Black,  however,  is  not  satisfactory.  His  tests  show  no  gain,  and  the  number  of  trials  for  each 
lesson  is  not  changing  much.  He  is  probably  merely  learning  the  answers,  and  needs  special 
study  and  assistance.     Look  out  for  and  avoid  records  of  this  type. 

The  Teacher's  Record  is  meant  for  your  own  use.  It  is  not  essential  to 
the  work,  except  that  by  means  of  it  you  can  prevent  children  saying  that 
they  handed  in  a  lesson  when  they  did  not.  It  is  also  of  value  in  erfabling 
you  to  systematize  the  assistance  you  give  to  individuals. 

Some  teachers  have  used  with  good  results  a  large  piece  of  cardboard 
ruled  to  correspond  to  the  record  in  the  Manual,  but  with  squares  large 
enough  to  permit  colored  or  gilt  stars  to  be  stuck  on  for  each  perfect  paper. 
Such  a  graphic  record  of  the  work  of  the  class  is  a  great  spur.  The  only 
objection  to  it  is  the  emphasis  v^hich  it  puts  on  the  number  of  lessons  com- 


16  -STANDARD     PRACTICE    TESTS 


pleted.  This  can  be  offset  somewhat  by  giving  to  the  child  who  has  made 
the  largest  gain  for  the  day  the  privilege  of  putting  on  the  stars  for  that  day. 
To  find  the  child  making  the  largest  gain,  ask  all  those  gaining  ten  examples 
or  more  to  raise  their  hands.  Then  go  up  the  scale,  11,  12,  13,  etc.,  or  down, 
9,  8,  7,  etc.,  until  but  a  single  hand  is  raised. 

Friday 
Lesson  1 
Ask  those  who  are  to  study  Lesson  1  to  raise   their  hands. 
Have  them  take  out  their  pads  and  begin  work.i 

If  they  prefer  to  practice  by  writing  the  answers,  let  them,  but  get  them 
started  before  giving  Lesson  2  to  the  other  children,  so  that  there  can  be  no  ques- 
tion of  their  practice  work  being  counted  as  a  test.  The  study  should  continue 
during  the  whole  time  the  other  children  are  taking  the  test,  scoring  the  papers, 
etc.  At  the  end  of  the  period,  comment  on  the  probable  gains  on  Monday  of  one 
or  two  individuals  who  have  studied  well,  or  who  have  wasted  their  time. 

This  study  period,  properly  handled,  can  be  used  to  prove  to  the  children 
the  value  of  ten  minutes  of  concentrated  effort.  Teaching  how  to  study  is  one 
of  the  most  important  features  of  a  teacher's  work.  From  this  time  on  some 
children  should  be  studying  and  some  taking  tests  each  day.  Out  of  a  class  of 
fifty  children,  therefore,  not  more  than  from  ten  to  twenty  perfect  papers  are 
likely  to  be  handed  in  on  any  one  day. 

Some  of  the  children,  particularly  after  a  few  days  when  the  children  begin 
to  see  the  possibilities  of  study,  will  want  to  practice  at  home.  In  general  this 
should  be  allowed,  but  only  when  it  results  in  gain.  There  is  such  a  thing  as 
over-training,  and  it  is  well  to  keep  track  of  the  effects  of  home  study.  The 
interest,  encouragement,  and  pride  of  parents  in  the  progress  of  the  child  are  some 
of  the  best  spurs  to  effort,  but  the  inordinate  ambitions  and  lack  of  appreciation  of 
the  efforts  the  child  may  be  making  are  also  some  of  the  most  harmful  influences. 

Lesson  2 
Give  and  score  Lesson  2,  following  the  procedure  for  Lesson  1. 
Those  who  have  perfect  papers  should  be  given  the  card  for  Les- 
son 3.  Those  who  fail  should  prepare  for  a  study  period  on 
Lesson  2.  Be  sure  each  day  to  have  ALL  record  their  scores  for 
the  day,  and  the  work  for  the  following  day. 

Monday 

Upt.to  this  time  the  drill  period  will  have  taken  25  or  30  minutes  each  day,  but 
beginning  with  the  second  week,  keep  a  score  in  your  record 
book  of  the  total  interval  from  the  time  you  first  say  ''Prepare  for 
Arithmetic  Drill "  to  the  time  you  are  ready  to  take  up  other  work. 

^  If  there  is  time  in  the  daily  program,  much  more  effective  work  can  be  done  by  having 
this  practice  and  study  done  during  a  regular  study  period,  so  that  every  child  is  ready  for 
a  test  every  day. 


^ TEACHER^S     MANUAL 17 

Make  this  period  a  drill  also  in  close  attention,  quick  actions,  and 
efficient  work.  At  the  end  of  two  weeks  the  drill  period  should  take  not 
more  than  ten  minutes  per  day  in  every  grade  except  the  4th.  Here  fifteen 
minutes  may  be  required.  To  spend  more  time  is  conclusive  proof  that 
your  control  of  the  class  or  your  power  of  organization  is  less  than  that 
of  hundreds  of  other  teachers  who  have  succeeded  in  keeping  within  the 
time  limits  given. 

On  this  day  there  may  be  four  groups  of  workers  in  your  class:  (1) 
children  excused  from  drill;  (2)  children  trying  Lesson  3  for  the  first  time; 
(3)  children  studying  on  Lesson  2;  (4)  children  trying  Lesson  1  for  the 
second  time.  From  this  time  on,  however,  the  children  themselves  will 
know  what  to  do  so  well  that  they  will  take  charge  of  their  own  work. 
Your  work  is  merely  to  time  the  test,  whether  the  children  are  on  Lesson  1 
or  10,  and  to  record  the  results. 

Be  sure  this  day  publicly  to  commend  the  children  who  studied 
Lesson  1  well  and  show  a  large  gain  in  today's  scores.  Emphasize 
GAIN  THROUGH  STUDY,  and  not  completion  of  the  lessons  only. 

Tuesday 

This  day  will  be  a  study  period  for  those  who  missed  Lessons  1, 
2,  and  3,  and  a  test  period  for  those  who  succeeded  on  Lessons  1,  2, 
and  3.     Follow  the  same  procedure  as  before. 

You  will  quickly  discover  that  one  or  two  children  need  to  be  watched 
in  regard  to  the  way  they  make  their  records,  one  or  two  in  planning  for 
the  work  they  are  to  take  next.  As  rapidly  as  possible  get  the  whole  pro- 
gram down  to  a  military  routine  in  charge  of  the  children  themselves. 
Omit  unnecessary  details,  such  as  standing,  raising  of  hands,  etc.,  and  have 
the  work  carried  through  with  the  least  possible  help  from  you.  In  three 
weeks  your  time,  from  the  end  of  the  test  interval  to  the  end  of  the  ten- 
minute  period,  should  be  free  for  helping  some  child  who  has  repeatedly 
failed.  In  a  month  or  six  weeks,  the  whole  drill  period  may  be  put  in 
charge  of  individuals  who  are  excused  from  drill,  thus  giving  them  valuable 
training  in  leadership  and  setting  your  time  free  from  individual  work.  A 
teacher  can  reach  a  final  efficiency  of  75-85%  by  systematically  helping  two 
children  a  day. 

Wednesday,  Thursday,  Friday 

No  further  instructions  are  necessary.  On  Friday  collect  all  the  Stu- 
dent's Records!  and  make  sure  the  records  are  being  properly  kept.  If  the 
above  program  has  been  followed,  each  book  should  contain  two  records 
for  Test  A  in  the  summary  on  page  5,  and  eight  records  opposite  the  first 
eight  days.  Two  sample  records  are  given  in  the  figures  on  the  following  page: 


18 


STANDARD     PRACTICE     TESTS 


Sample  Records 


Boy  A 


Boy  B 


c 

Scores 

G 

Scores 

Q 

^3 

■♦-* 

o 

TJ 

4^ 

& 

s 

x>D 

I 

4> 

J3 

Q 

J 

H 

2 

Q 

hJ 

H 

C^ 

1 

1 

72 

72 

1 

32 

25 

2 

2 

C5 

CO 

2 

Pr 

Pr 

3 

Pr 

Pr 

3 

32 

•   30 

4 

2 

70 

69 

4 

Pr 

Pr 

5 

2 

Pr 

Pr 

5 

43 

43 

6 

2 

70 

70 

6 

Pr 

Pr 

7 

3 

07 

67 

7 

51 

50 

8 

4 

70 

70 

8 

Pr 

Pr 

Monday 


Omit  the  drill   on  this   day  and  spend  the  time  teaching  the 
children  to  graph  their  scores. 

Prepare  on  the  board  a  copy  of  the  first  graph  page  (page  10  in  the 
Student's  Record).  Select  some  child  who  had  a  low  score  in  Lesson  1  at 
the  start,  and  who  has  made  a  good  gain,  but  has  not  completed  the  lesson. 
If  there  are  none  in  the  class,  use  the  scores  of  Boy  B  in  the  illustration 
above.  Copy  the  record  on  the  board.  Tell  the  children  that  you  are  going 
to  show  them  how  to  draw  a  picture  of  these  scores,  that  they  may  all  see  the 
gain  that  is  being  made.  Have  them  all  turn  to  page  10  and  find  the  column 
marked  "1st  Trial."  Point  to  the  score  for  the  number  tried  (32  in  the  illus- 
tration, on  the  following  page)  and  have  the  children  move  their  pencils  up 
the  column  until  they  find  this  number,  then  draw  a  short  horizontal  line 
through  it.  Illustrate  your  instructions  in  the  diagram  on  the  board.  In  sim- 
ilar fashion  have  the  score  for  each  trial  found  and  marked.  The  children 
should  then  use  their  rulers  and  draw  a  line  from  one  number  to  the  next. 
The  result  of  the  reqord  above  will  look  like  the  figure  on  the  following  page. 


TEACHER'S  MANUAL  19 


Graph  Sheet 

FOR 

Lesson 

No. 

1.     . 

.72 

examples 

Lesson  No. 

2... 

.70 

examples 

Lesson 

No. 

3... 

67 

examples 

Lesson  No. 

4... 

.70 

examples 

LESSO 

N.NO. 

73       7a 

7a 

73 

73 

73 

73 

73 

73 

73 

73 

73 

73 

73         73 

71         71 

71 

71 

71 

71 

71 

71 

71 

71 

71 

71 

71         71 

70         70 

70 

70 

70 

70 

70 

70 

70 

70         70 

69         S9 

69 

69 

89 

69 

69         69 

68         68 

68 

68 

68 

68 

68 

68 

68 

68 

68 

68 

68 

68         68 

67         «7 

67 

67 

67 

67 

67 

67 

67         67 

66         66 

66 

66 

66 

66 

66 

66 

66 

66 

66 

66          63 

6S         65 

6S 

6S 

65         65 

e*      64 

64 

64 

64 

64 

64 

6t 

64 

64 

64 

64 

64 

64         64 

«3         63 

63 

63 

63 

63 

63 

«i 

63 

63 

63 

63 

63 

63 

63 

63 

63 

63 

63 

6a 

63         63 

61         61 

61 

61 

61 

61 

61 

61 

61 

61 

61 

61 

61 

88 

68 

58 

58 

58 

SS 

58 

58 

58 

SS 

58 

S8 

58 

58 

67 

57 

57 

57 

57 

56' 

56 

56 

56 

56 

56 

56 

56 

58 

SM 

SS 

SS 

65 

5S 

55 

SS 

55 

55 

SS 

SS 

53 

53 

53 

53 

S3 

S3 

S3 

S3 

S3 

53 

53 

SI 

51 

51 

/«- 

51 

51 

51 

51 

r* 

SO 

SO 

SO 

SO 

SO 

SO 

SO 

SO 

48 

49 

49 

49 

49 

49 

49 

48 

48 

48 

48 

48 

48 

4B 

48 

48 

48 

47 

47 

47 

»47 

47 

47 

47 

47 

47 

46 

46  1 

46 

46 

46 

46 

46 

46 

46 

46 

46 

45 

45 

45 

45 

45 

4S 

45 

45 

45 

45 

44 

44 

^ 

44 

44 

44 

44 

44 

44 

44 

37  I  37    37    37 


31    31/   31    31    31    31    31    31    31    31    31    31    31    31 


INSTRUCTIONS:  After  each  trial,  in  the  column  corresponding  to  the  num- 
ber of  the  trial,  draw  a  short  horizontal  line  through  your  score  in  examples 
trud.  Usmg  a  ruler,  draw  a  heavy  line  from  this  point  to  the  score  marked  in 
the  previous  column.  In  hke  rranner  draw  a  curve  for  Rights,  using  a  heavy 
broken  line.  More  than  one  graph  can^be  drawn  on  this  page;  see  Model,  page 
7.  When  you  have  completed  the  lesson  successfully,  hand  in  this  record  book 
with  your  paper. 

The  dotted  line  is  drawn  in  precisely  similar  fashion  to  represent  the  scores 
for  rights. 

Discuss  the  meanings  of  the  ups  and  downs  of  the  figures  until  the 
children  are  able  to  "read"  the  curves  easily.  Then  put  a  second  series  of 
scores  on  the  board  and  have  the  graphs  drawn,  or  let  the  children  who 
have  tried  any  test  three  times  or  more  draw  the  graph  of  their  own  scores. 

From  this  time  on,  at  the  end  of  the  drill  period  each  day,  ask  **How 
many  have  tried  the  lesson  they  are  on  three  times?  Start  your  graphs." 
Then,  "How  many  have  tried  the  lesson  they  are  on  five  times  or  more? 
Bring  me  your  graphs." 

Ordinarily  but  one  or  two  children  will  come  forward.  Have  them  bring 
their  record  books  to  you  open  in  such  a  position  that  the  graph  is  right  side 
up  to  you.^  You  can  then  see  at  a  glance  whether  their  scores  are  rising  or 
falling.  Praise  those  whose  scores  have  gone  up.  Retain  the  books  of  those 
whose  scores  for  several  days  have  shown  no  gain,  or  a  loss.  A  single  low 
score  may  have  no  meaning.  Low  scores  are  often  made  just  before  a  big 
gain.  But  three  days  of  low  scores  or  three  days  without  any  gain  means 
almost  without  exception  that  the  child  is  merely  wasting  his  time.     It  is 


^The  graph  for  the  score  for  the  day  should  of  course  be  drawn  first. 


20 STANDARD     PRACTICE     TESTS 

better  for  him  to  have  no  drill  at  all  than  merely  to  go  through  the  motions 
without  benefit  day  after  day.  A  child  should  be  permitted  to  try  a  lesson 
fifteen  or  twenty  times,  or  more,  as  long  as  he  is  steadily  gaining,  even  though 
the  gain  is  small,  but  it  is  criminal  to  let  a  child  keep  on  wasting  his  time  or 
)ven  injuring  himself  by  improper  study  and  effort. 

Therefore,  stop  the  drill  of  such  children  until  you  have  time  to 
work  with  them  as  individuals,  and  either  diagnose  the  trouble  (see 
pages  27-44)  or  make  some  radical  change  in  the  method  of  study 
being  followed. 

When  no  diagnosis  can  be  made,  either  from  lack  of  time  or  because 
the  cause  of  the  difficulty  is  obscure,  it  is  a  good  plan  to  let  the  child  go 
on  to  the  next  lesson  for  a  time.  For  some  children,  intermittent  practice 
on  three  or  four  lessons  seems  to  be  better  than  continuous  practice  on  one 
lesson. 

The  graphs  tell  the  whole  story  of  a  child's  progress  at  a  glance,  and  no 
teacher  can  afford  to  neglect  this  feature  of  the  work.  If  done  systematically, 
it  will  take  less  than  half  a  minute  each  day  to  select  the  children  in  need  of 
assistance.  The  children,  after  once  starting  a  graph,  add  to  it  each  day 
immediately  after  recording  their  scores. 

No  further  instructions  are  necessary.  The  mechanical  features  of  tbe 
work  should  become  more  and  more  routine,  and  the  teacher  should  be  able 
to  give  his  time  and  attention  more  and  more  to  the  direct  personal  assistance 
needed  by  the  children  who  fail.  The  teacher's  true  function  is  this  giving 
of  assistance  and  encouragement,  and  his  success  will  depend  directly  upon 
how  thoroughly  he  discharges  it.  Therefore,  the  remainder  of  the  manual 
will  be  devoted  to  giving  such  directions  as  are  possible  for  dealing  with  the 
common  difficulties  which  children  are  likely  to  have  in  working  on  these 
lessons. 

Section  III 
Diagnosis  and  Remedy  of  Individual  Defects 

In  the  following  pages  will  be  found  a  discussion  of  some  of  the  more 
common  difficulties  which  occur  in  working  with  children,  together  with 
suggestions  for  dealing  with  the  same.  The  teacher  should  read  these, 
through  rapidly  so  that  he  may  know  the  general  content,  but  they  will 
require  careful  reading  only  as  the  need  arises.  In  the  same  way,  when  a 
child  has  difficulty  with  a  particular  lesson,  read  the  comments  on  that 
lesson;  for  each  is  designed  to  bring  to  light  and  to  remedy  a  particular 
difficulty. 

General  Difficulties 

Cheating.  Some  children  always  have  cheated,  and  some  children 
always  will.     However,  the  teacher  should  do  his  utmost  to  develop  ideals 


TEACHER^S     MANUAL 21 

of  honesty  and   self-mastery,   and  should  value  the  opportunities   for   moral 
training  which  the  Practice  Tests  provide. 

One  form  of  cheating  consists  in  learning  the  answers  by  heart,  and 
writing  them  in  place  without  doing  the  work.  Even  in  honest  study  on  the 
same  test  day  after  day,  there  is  danger  that  the  answers  will  be  impressed 
upon  the  mind.  The  remedy  is  to  work  the  examples  in  a  different  way  each 
day;  one  day  from  the  left  of  the  sheet  to  the  right,  another  from  right  to  left, 
the  next  from  top  to  bottom,  and  so  on.  If  in  spite  of  changing  the  order 
of  work,  a  child  complains  of  knowing  the  answers,  have  him  change  from 
Form  A  to  Form  B,  and  vice  versa.  This  is  one  of  the  reasons  for  supplying 
the  tests  in  two  different  forms.  If  children  understand  that  they  must  really 
gain  in  ability  from  their  practice  so  much  that  after  they  have  completed 
Form  A  of  any  lesson,  they  will  be  able  to  do  Form  B  successfully  also,  it 
will  go  a  long  way  towards  eliminating  the  cheating.  In  other  words,  the 
remedy  for  cheating  is  to  detect  it,  and  to  substitute  the  right  ideal  for  the 
poor  one. 

In  similar  fashion,  when  sudden  and  remarkable  gains  are  made  so  that 
cheating  is  suspected,  give  the  child  the  other  form  of  the  same  lesson,  and 
let  the  test  be  conducted  under  your  immediate  supervision.  If  the  child's 
scores  fall  to  the  old  level,  it  is  almost  a  certain  sign  of  cheating.  The 
penalty  should  be  to  begin  again  at  the  beginning. 

Another  form  of  cheating  is  the  writing  of  the  answers  on  the  tissue- 
paper  sheet.  Some  children  will  even  try  putting  the  lesson  card  in  place 
answer  side  up.  To  detect  this,  walk  through  the  aisles  at  the  time  of  the 
test  and  make  sure  the  cards  are  put  in  position  correctly.  Where  this  form 
of  cheating  is  suspected,  once  in  a  while  have  the  children  get  all  ready  for  a 
test,  then  instead  of  giving  the  signal  "Start,"  collect  the  pads  and  spend  the 
ten  minutes  looking  through  the  papers. 

A  more   difficult  form  of  cheating  to  detect  is  the  careful  preparation 
beforehand  of  perfect   papers,   and  the  substitution  of  such   papers   for  the 
paper  actually  written  during  the  class  time.    A  test  under  close  supervision 
^will  be  effective  here  also. 

I^K^  Teachers  should  exercise  great  vigilance  at  all  times,  as  children  love  to 
"  boast  of  fooling  the  teacher,  and  are  sure  to.  defend  themselves  by  the 
statement  that  "Every  one  in  the  room  does  it."  Unfortunately  too  few 
adults  know  how  to  interpret  such  statements  correctly,  and  the  effect  on 
the  teacher's  reputation  is  disastrous.  Take  it  for  granted  that  every  child 
is  honest  and  if  you  speak  of  the  subject  at  all,  discuss  it  from  the  side  of 
ideals  of  honesty,  growth,  and  self-mastery.  At  the  same  time,  be  wise  and 
vigilant.  Suspect  especially  those  children  who  do  well  in  the  daily  drills, 
but  fail  on  the  tests  or  in  their  regular  arithmetic  work. 


22 STANDARD     PRACTICE    TESTS 

Transfer.  Another  serious  problem  is*  the  question  of  transfer.  It  is 
well-nigh  inconceivable  that  a  child  can  do  perfect  work  in  the  drills  day- 
after  day,  yet  fail  in  the  tests'  or  in  regular  arithmetic  work,  but  laboratory 
experiments  i^rove  that  for  some  children  the  slightest  change  in  the 
most  trivial  conditions  under  which  work  is  done  is  enough  to  throw  well- 
fixed  habits  out  of  gear.  Apparently  the  remedy  is  to  bring  the  possibility  of 
transfer  to  the  conscious  attention  of  the  child.  If  he  is  careless  in  regular 
work,  have  him  prepare  the  examples  of  the  lesson  for  any  day  in  the  form 
of  one  of  the  lesson  cards,  and  have  him  practice  it  until  he  can  do  it 
perfectly.  The  teacher  must  keep  consistently  to  the  position  that  imless  the 
speed  and  accuracy  of  the  drill  work  transfer  to  other  situations,  they  are 
valueless. 

In  this  connection,  the  teacher  will  do  well  to  call  the  attention  of  the 
pupils  to  the  difference  between  their  habits  of  study  and  work  on  their 
ordinary  lessons  and  on  the  drill  lessons.  The  wise  teacher  will,  from  time 
to  time,  give  set  tasks  to  be  completed,  and  set  lessons  to  be  studied,  in  a 
given  time.  Both  children  and  adults  should  constantly  strive  for  maximum 
concentration  of  attention  and  effort  during  their  working  periods. 

Efficiency.  The  term  "efficiency"  has  been  used  so  loosely  in  educational 
discussions  as  to  be  almost  meaningless,  but  the  adoption  of  definite  standards 
of  achievement  makes  possible  scientific  definition.  By  the  efficiency  of  any 
test  will  be  meant  the  per  cent  the  perfect  papers  are  of  the  total  number;  by 
the  efficiency  of  the  teaching  during  any  period,  the  per  cent  the  children 
who  attain  standard  ability  are  of  the  total  number  below  standard  at  the 
start. 

For  instance,  if  in  a  class  of  fifty,  five  children  are  perfect  in  Test  A 
at  the  beginning  of  the  term,  the  efficiency  of  the  test  is  5/50  or  10%.  If, 
after  seven  weeks'  work.  Test  A  is  given  again  and  thirty  children  have 
perfect  papers,  the  efficiency  of  the  second  test  is  30/50  or  60%.  The  efficiency 
of  the  teaching  is  55%.  That  is,  there  were  45  children  below  standard 
at  the  beginning  and  25  children  have  been  brought  up  to  standard  by  the 
teaching.  The  efficiency  is  25/45  or  55%.*  Such  a  measurement  of  efficiency 
is  open  to  the  objection  of  unequal  units,  since  to  raise  one  child  to  the 
standard  is  not  the  same  as  to  raise  to  the  standard  another  child  of  very 
different  initial  ability.  Practically,  however,  for  all  unselected  classes  of 
twenty  children  or  more,  the  objection  of  unequal  units  is  not  valid. 

Teachers  interested  in  their  own  professional  ability  should  measure 
carefully  the  efficiency  of  their  teaching  year  after  year.  To  be  sure,  it 
sometimes  takes  courage  to  face  the  disagreeable  truth,  for  present-day 
efficiencies  are  low ;  but  without  such  measures  it  is  impossible  to  tell  whether 
one  is  improving  or  not.     Particularly  valuable  would  be  comparisons  of  the 


*  For  practical  purposes  it  is  sufficient  to  subtract  initial  from  final  efficiency ,- 
60%— 10%=50%. 


,     TEACHER^S     MANUAL 23 

efficiency  of  different  methods  used  by  the  same  teacher  with  different  groups 
of  children  of  the  same  grade,  and  of  approximately  equal  initial  ability. 

Types.  The  diagnosis  of  educational  ills  and  the  prescription  of  appro- 
priate remedies  is  foreign  to  the  average  teacher's  thinking  and  practice. 
To  aid  in  this  work  each  lesson  of  the  Practice  Tests  has  been  made  to 
reveal  and  remedy  a  different  difficulty.  Unfortunately,  however,  there  are 
certain  general  defects  which  operate  to  obscure  the  smaller  difficulties,  and 
many  of  these  are  due  to  the  fact  that  individual  children  exhibit  extreme 
mental  and  physical  peculiarijties.  In  the  discussions  which  follow,  however, 
nothing  should  be  construed  as  meaning  that  a  class  can  be  divided  into 
groups  of  different  types  which  can  be  handled  as  groups,  each  in  its  own 
way.  For  nothing  is  farther  from  the  truth.  Each  individual  is  a  law 
unto  himself  and  is  better  able  to  detect  the  methods  of  study  and  work 
best  suited  to  his  needs  than  any  teacher.  Just  ask  yourself  how  far  you 
would  be  willing  to  have  some  one  else  determine  what  you  are  to  eat,  or 
read,  or  how  you  should  spend  your  time.  So  in  school  the  demand  of 
teachers  for  the  use  of  certain  methods,  or  certain  orders  of  growth,  is  just 
as  irksome  to  the  children.  The  proper  thing  to  do  is  to  set  the  desired 
goal  before  the  child,  and  let  him  choose  his  own  method  of  reaching  that 
goal.  The  teacher,  however,  needs  to  have  a  sympathetic  understanding  of 
what  is  going  on  in  the  mind  of  the  child,  that  he  may  make  the  adjustments 
proper  to  the  method  chosen.  Therefore,  the  effect  of  various  factors 
sometimes  operating  will  be  discussed. 

Age.  In  nearly  every  class  will  be  found  young,  precocious  children  and 
over-age,  retarded  children.  Unfortunately,  physiological  age  and  psycho- 
logical age  do  not  always  agree.  A  child  may  have  a  mind  so  keen  and  alert 
that  he  can  understand  perfectly  sixth-grade  work  at  the  age  of  ten,  yet  his 
bones  and  muscles  may  be  no  more  mature  than  those  of  other  children  of 
ten.  For  such  children  the  standards  of  speed,  if  not  easily  attained,  should 
be  lowered  to  correspond  to  their  muscular  age,  whatever  that  may  be;  that 
is,  lowered  to  a  standard  that  can  be  easily  reached  with  ordinary  effort.  In 
other  words,  when  a  child  has  difficulty  in  reaching  the  required  speed,  if  he 
is  also  under  age,  or  gives  evidence  of  immaturity  for  his  years,  lower  the 
standard  so  that  the  task  set  is  within  his  reach. 

On  the  other  hand,  the  over-age  child  is  usually  slow  in  developing.  Be 
content  with  slow,  steady  gains,  but  push  the  practice  as  far  as  you  can. 
Physically  he  will  be  capable  of  standing  a  large  amount  of  drill,  but  the 
returns  from  the  time  expended  will  be  small.  Be  sure  to  reward  such 
gains  in  proportion  to  effort  and  not  to  amount. 

Temperament.  There  are  three  extremes  of  temperament  to  be  noted. 
One  of  these  is  the  hasty,  energetic  child,  careless  and  inaccurate  in  all 
school  work,  and  often  difficult  to  manage.  Such  children  will  respond  to 
the  element  of  "record  breaking"   in   drills,   and   do   unusually   well.     It  is 


24 STANDARD     PRACTICE     TESTS 

common  experience  to  find  a  child,  classed  as  dull  and  difficult  in  ordinary 
school  work,  leading  the  class  in  drills.  This  merely  indicates  that  the  child 
has  natural  ability  and  can  do  well  when  he  chooses  to  exert  himself,  but 
that  the  ordinary  work  of  the  school  has  made  no  appeal  to  him.  Children 
of  this  type  will  develop  in  speed  first,  then  slowly  bring  up  their  accuracy. 

The  other  extreme  is  the  phlegmatic  child  who  insists  upon  having 
everything  he  does  exactly  right,  but  is  correspondingly  slow.  Such  chil- 
dren grow  slowly  in  speed,  and  need  the  ideal  of  rapid,  efficient  action  as 
much  as  the  other  type  need  ideals  of  conscientious  accuracy.  The  teacher 
is  called  upon  to  appreciate  the  struggles  of  both  and  should  let  each  grow 
in  his  own  way,  commending  the  gain  of  one  in  speed  as  much  as  the  gain 
of  the  other  in  accuracy.  It  is  the  appreciation  of  effort,  and  encouragement 
at  points  of  difficulty,  that  make  a  teacher's  work  successful. 

The  third  type  Is  the  nervous,  self-conscious  child  who  "goes  to  pieces"  on 
all  examinations,  and  consequently  dreads  and  hates  the  drill  work.  The 
difficulty  to  be  overcome  here  is  not  mathematical  at  all,  and  the  remedy 
is  less  difficult  than  might  be  imagined.  Give  such  children  permission  not 
to  take  the  tests  on  any  day  they  feel  themselves  getting  nervous.  Give 
them  trials  alone  before  or  after  school,  if  necessary,  but  always  keep  to 
the  front  the  ideal  of  the  development  of  such  self-mastery  that  they  will 
be  able  to  take  their  tests  with  the  class.  The  method  here  is  suggestion 
and  physical  training.  Call  the  attention  of  the  child  to  the  fact  that  when 
he  is  "nervous"  his  muscles  are  always  tense  and  his  breathing  shallow. 
Show  him  how  to  relax,  and  how  to  breathe  deeply.  Interrupt  his  test  at  the 
least  sign  of  nervousness,  with  the  suggestion  "Relax,"  "Take  a  deep  breath." 
Make  the  point  that  mastery  of  himself  is  more  important  than  the  mastery 
of  the  drill  lesson,  and  the  child  will  soon  respond.  No  more  valuable 
assistance  can  be  rendered  by  a  teacher  than  the  delivery  of  such  a  child 
from  the  habit  of  worry,  and  the  development  of  poise  and  control. 

Physical  Condition.  The  effect  of  this  factor  is  too  often  disregarded 
by  teachers.  On  the  one  hand,  they  are  likely  to  take  to  themselves  credit 
for  the  rapid  mental  progress  shown  by  certain  children  in  their  classes, 
when  the  real  reason  for  growth  is  merely  that  the  children  have  reached 
a  growth  stage  in  their  development  and  could  not  possibly  be  kept  from 
learning;  and  on  the  other  hand,  they  are  likely  to  be  unduly  discouraged 
by  the  failure  of  certain  children  to  respond  to  their  efforts. 

The  truth  of  the  matter  is  that  there  seem  to  be  in  some  children  well- 
marked  periods  of  rapid  mental  growth,  and  conversely  there  may  be  long 
periods  where  normal  practice  seems  to  produce  no  results.  The  teacher's 
task  is  at  best  a  difficult  one,  and  when  one  has  done  everything  one  knows* 
how  to  do,  and  the  scores  of  what  is  apparently  a  normal  child  remain 
stubbornly  constant,  it  is  sometimes  comforting  to  know  that  at  least  the 
practice  may  be  preparing  for  a  period  of  rapid  development  severa!! 
months  later.    Just  as  a  physician  has  many  cases  which  he  is  unable  to  cure. 


TEACHER^S     MANUAL 25 

so  the  teacher  will  have  many  children  where  the  difficulty  will  resist  every 
effort  to  remove  it. 

In  cases  where  a  child's  memory  is  variable,  where  on  some  days  the 
child  does  well,  and  seems  to  make  good  progress,  and  on  other  days"  to 
lose  the  gain  and  do  poorly,  suspect  some  physical  disturbance.  Inquire 
as  to  home  conditions,  food,  sleep,  recent  disease,  etc.  In  poor  districts, 
children  are  often  required  to  labor  long  hours  after  school,  and  with  loss 
of  sleep,  insufficient  food,  and  physical  exhaustion  there  is  little  energy  left 
for  school  work.  Until  we  have  state  control  of  the  conditions  of  child  life 
out  of  school  hours,  little  can  be  done  in  such  cases  unless  teacher  or  prin- 
cipal cares  to  give  personal  time  and  attention  in  trying  to  remedy  the  social 
conditions  in  the  home. 

Severe  4isease  may  operate  to  weaken  memory  and  Intellectual  powers 
for  several  years.  It  rnay  also  serve  as  a  stimulus  to  growth.  In  cases  of 
impaired  memory,  the  teacher  should  not  be  discouraged  by  frequent  slumps 
and  lapses.  If  the  practice  is  continued  through  t\yo  or  three  years,  the 
time  will  finally  come  when  normal  conditions  will  be  attained. 

The  period  from  11  to  13  (eighth  grade)  is  a  difficult  period,  particularly 
for  girls.  Great  physical  changes  are  taking  place  in  the  body,  and  new  im- 
pulses and  ideas  are  making  themselves  felt  in  the  mind.  Unfortunately,  also, 
school  work  at  this  age  is  often  a  deadly,  mechanical  grind.  The  develop' 
ment  curves  of  many  school  abilities  frequently  show  marked  drops  at  the 
sixth  grade.  Experiments  seem  to  prove,  however,  that  the  cause  is  wholly 
mental.  If  the  work  makes  sufficient  appeal,  the  sixth  grade  may  be  a  place 
of  unusual  growth.  Keep  the  play  element  uppermost,  and  make  the  drills 
"fun." 

Mental  Traits.  Children  differ  markedly  In  their  natural  aptitudes.  The 
two  extremes  most  often  noted  by  teachers  are  the  mechanical  and  the  rea- 
soning types.  In  nearly  every  class  there  will  be  some  one  child  who  leads 
the  class  in  the  drill  work,  but  who  falls  away  behind  on  the  problem  work. 
There  is  often  also  a  child  of  marked  intellectual  understanding  who  is 
slow  and  inaccurate  in  the  drills. 

The  Practice  Tests  are  admirably  suited  to  handling  such  children. 
Praise  the  mechanically  minded  child  and  help  him  in  every  way  you  can 
to  finish  the  drill  work  and  to  feel  that  he  is  succeeding.  Then  give  him 
special  assignments  in  the  problem  work,  to  be  studied  in  the  drill  period. 
Take  these  assignments  from  the  second-grade  work  if  necessary,  but  have 
them  within  the  reach  of  the  child's  understanding,  and  carry  him  along 
slowly  and  successfully  for  a  time  in  the  problem  work.  The  time  will  soon 
come  when  he  will  make  rapid  growth. 

On  the  other  hand,  It  Is  of  the  utmost  Importance  that  a  child  of  great 
reasoning  powers  should  not  be  handicapped  by  poor  habits  of  work  in  the 
Work  he  is  capable  of  doing.  If  such  a  child,  through  the  persistent 
efforts  of  a  teacher,  finally  attains  to  efficient  control  over  the  mechanical 


26 STANDARD     PRACTICE     TESTS 

skills,  his  productivity  as  a  mature  individual  will  be  greatly  increased.  Be 
very  strict,  but  patient,  with  such  children.  Accuracy  will  be  hard  for 
them  to  acquire,  but  no  other  class  of  children  will  ultimately  give  so  great 
a  return  for  efforts  expended. 

Speed.  Every  individual  is  capable  of  working  at  very  different  speeds, 
yet  every  individual  probably  has  his  own  normal  speed.  In  demanding  a 
certain  rate  of  work  from  the  children,  the  idea  is  not  at  all  to  "speed  them 
up";  that  is,  make  them  work  at  high  tension.  The  speed  that  is  demanded 
is  the  average  or  natural  speed  for  a  given  grade  as  determined  by  the 
measurement  of  many  thousands  of  children  of  that  grade.  A  child  who 
cannot  make  this  speed  without  strain  will  ordinarily  be  found  to  be  inaccu- 
rate in  his  work,  or  to  have  poor  habits  of  work.  It  takes  time  to  make 
mistakes.  Speed  in  addition,  for  instance,  means  the  existence  of  a  com- 
plex habit,  means  that  there  has  been  sufficient  repetition  to  render  various 
component  actions  which  enter  into  the  habit  automatic  and  perfect.  Too 
many  teachers  do  not  know  the  value  of  the  repeated  working  of  a  single 
example,  until  the  habit  of  automatic  action  has  been  established.  When 
signs  of  a  strain  to  make  a  given  speed  are  evident,  break  the  test  up  into 
small  sections — a  single  example,  then  two,  four,  etc.  Have  these  practiced 
until  the  child  knows  them  by  heart,  until  they  can  be  worked  through 
smoothly  at  high  speed  without  strain.  Keep  up  the  practice  until  all  parts 
of  a  test  have  been  so  handled,  and  finally  the  speed,  not  only  for  that  test, 
but  for  other  and  more  difficult  tests,  will  be  found  to  have  reached  the 
proper  level. 

One  exception  to  the  above  is  to  be  noted.  Some  children  are  born 
with  nerves  and  muscles  predestined  to  slower  action  than  normal.  Very 
little  can  be  done  in  such  cases,  and  the  standard  should  be  reduced  to  the 
level  of  such  children's  ability.  The  one  thing  the  writer  can  suggest  is  to  set 
the  new  standard  slightly  above  their  present  achievements,  and  little  by 
little  raise  the  speed.  Such  children,  of  course,  have  to  work  at  higher 
nerve  tension  than  normal  children,  if  they  are  to  overcome  their  natural 
handicap  of  slowness,  but  one  should  be  careful  to  demand  but  a  very 
gradual  increase  in  speed. 

Mental  Deficiency.  Much  attention  is  now  being  paid  to  the  organization 
of  special  classes  for  backward  and  defective  children,  but  teachers  should 
be  careful  not  to  be  hasty  in  assuming  that  a  child's  poor  work  is  due  to 
this  cause.  The  perfectly  balanced  child,  either  mentally  or  physically,  is 
very  rare.  All  have  mental  tendencies  and  bias  which  in  degree  are 
worthy  of  the  name  mental  defects.  Measurement  has  shown  that  a  child 
may  be  able  to  learn  addition  easily,  yet  have  great  ditficulty  with  subtrac- 
tion, while  for  the  next  child  it  may  be  subtraction  that  is  easy  and  addition 
that  is  hard.  Such  tendencies  are  passed  along  from  parents  to  children  in 
precisely  the  same  fashion  as  red  hair  or  blue  eyes.  The  teacher  should 
note  particularly  that  where  such  defects  operate  to  hinder  the  development 
of  the  child  in  the  elementary  grades,   a   condition   of  mental   retardation 


TEACH  ER^S     MANUAL 27 

often  arises  which  makes  the  child  seem  wholly  defective.  If  you  have 
such  children  in  your  class,  watch  them  closely  to  discover  in  what  they 
are  interested,  what  kind  of  activities  they  can  do  well.  Give  them  as  much 
as  possible  of  such  work.  Once  a  door  has  been  found  into  the  mind,  very 
rapid  development  may  take  place  along  many  other  lines,  and  the  child  may 
finally  approximate  normal  conditions. 

Miscellaneous.  It  would  be  impossible  to  list  all  the  special  and  peculiar 
difficulties  which  fall  within  the  experience  of  any  grade  teacher,  and  each 
worker  must  depend  upon  his  own  powers  of  observation  to  discover,  and 
his  own  ingenuity  to  invent,  methods  of  treatment  for  the  same.  Certain 
difficulties,  however,  are  inherent  in  the  four  processes  themselves,  and 
these  the  Practice  Tests  are  designed  to  remedy.  Each  lesson  will  now  be 
discussed  in  detail. 

Practice  Lessons 

Lesson  1.     Subject,  Addition 

Special  Phase,  Knowledge  of  the  Combinations 

The  examples  in  this  lesson  represent  the  next  step    Typical  examples 

beyond  the  addition  combinations,  and  it  is  the  belief 

of  the  author  that  the  combinations  should  be  learned 

by  practicing  such  examples.     There  is  evidence  that 

it   takes   longer   to    study    the    separate    combinations, 

and  then  learn  to  add,  than  it  does  simply  to  learn  to     "~  — "  ""  "^ 

add.     For  the  use  of  those  teachers  who  take  the  op~ 

posite  view,  the  hundred  fundamental  combinations  are  given  in  Lesson  45, 

together   with    tests    for   the    same.     The    answers   to    these    should   not   be 

written,  but  recited  orally.     To  prove  to  a  child  that  he  does  not  know  his 

combinations,   have    him   put   the    test    card    in    his   pad   and    write   all   the 

answers.     Then,  with  the  answers  in  position,  find  the  time  required  for  him 

simply  to  read  the  answers.    Remove  the  card  and  find  the  time  required  to 

give  the  answers    from    memory.     Unless  the    two    times    are    closely    the 

same,   the  child's  speed   and   accuracy  may  be  benefited  by  a   study  of  the 

combinations'.     Note  that  on  the  test  card  the  fundamental  facts  are  divided 

into  three  groups,   so  that  a   child  need  waste  no  time  on  groups  that  he 

already  knows.    Do  not  let  him  say,  "Five  and  four  are  nine."    Teach  him 

to  read  the  answers  only.    Thus,  for  the  combinations  shown  in 

the   margin   the   child   should   neither   think   nor   say   more   than        4    9     2 

"9,  17,  8."    He  must  read  the  answers  in  exactly  the  way  that  he        5     8     6 

reads  words  without  spelling  the  letters.  "" 

As  soon  as  a  child  by  study  has  decrease3  the  time  required  to  recite 
from  the  test  card  the  answers  to  the  combinations,  try  him  again  on  Lesson 
jl.  If  his  scores  show  no  improvement,  it  is  proof  positive  that  for  him 
the  study  of  the  separate  combinations  has  not  been  of  value.     Only  about 


6 

8     9     6 

4 

5     3     8 

7 

2     1     4 

28 STANDARD     PRACTICE    TESTS 

three  or  four  children  out  of  ten  will  profit   much  by  such  a   direct  study 
of  the  combinations. 

A  better  plan  is  to  have  the  child  practice  directly  on  the  examples  in 
the  lesson.  Have  him  add  aloud  one  example  until  he  knows  it  by  heart. 
Then  take  two,  three,  one  row,  two  rows,  etc.,  until  the  child  can  do  a  limited 
portion  of  the  test  satisfactorily.  He  will  then  know  what  is  expected  of 
him  and  how  to  study,  so  that  he  may  be  left  to  his  own  study,  the  teacher 
following  the  effect  of  his  efforts  from  the  graph  of  his  daily  scores.  In 
practicing  on  Lesson  1,  have  the  child  add  from  the  bottom  to  the  top  of 
each  example.  When  these  additions  become  too  familiar,  reverse  the  order 
and  let  him  add  from  top  to  bottom.  Be  sure  to  emphasize  the  need  of  adding, 
not  merely  remembering  the  answers. 

Many  teachers  object  to  giving  the  child  the  same  examples  to  work 
over  and  over  again.  They  feel  that  mere  memory  of  the  results  in  a 
particular  example  is  of  no  value.  This  is  wrong.  In  each  form  of  Lesson 
1  all  the  important  combinations  occur  at  least  once,  and  many  twice.  If  a 
child  practices  on  Lesson  1,  Form  A,  until  he  knows  it  by  heart,  and  is 
then  tested  with  Form  B,  his  scores  will  show  a  surprising  gain  although 
the  examples  are  not  the  same  in  the  two  tests.  In  similar  fashion,  by  the 
time  he  has  learned  by  heart  all  the  addition  lessons  in  the  series,  he  will 
have  covered  the  combinations  in  so  many  different  arrangements  that  no 
new  material  can  be  given  him  that  he  will  not  be  able  to  add  without 
study.  However,  each  teacher  will  have  to  experiment  and  prove  these 
statements  for  himself.    For- very  many,  conviction  is  born  of  experience  only. 

The  surest  symptom  of  lack  of  knowledge  of  the  combinations  is  count- 
ing. Look  out  for  counting  with  fingers,  toes,  tongue,  nodding  the  head,  etc. 
By  practice  on  one  example  until  it  is  learned  by  heart,  convince  the  child 
that  it  is  both  quicker  and  easier  "to  remember"  than  "to  count."  Even 
the  most  persistent  counters  will  have  a  few  simple  combinations  which 
they  do  not  count,  and  these  may  be  used  as  a  basis  of  explanation. 

Children,  often  have  difficulty  with  particular  combinations,  as  7-|-8 
or  9-}-4.  If  repeated  practice  fails  to  break  down  such  difficulty,  use  one 
of  the  roundabout  methods,  as  breaking  the  4  into  3+1,  adding  the  9  to 
the  1,  and  then  adding  the  3  to  the  sum.  Or  try  to  establish  some  associa- 
tion, as  the  sum  of  any  number  and  nine  is  always  one  less  unit  in  the  next 
tens, — 4,  13.  But  such  methods  should  never  he  used  except  as  a  last  resort. 
Every  thought  takes  time  and  energy,  and  it  is  wrong  to  make  a  child 
think  two  thoughts  to  get  a  given  sum  when  one  will  do. 

Children  occasionally  fail  in  this  test  for  other  reasons.  One  of  the 
brightest  children  in  a  certain  class  made  almost  no  progress  in  Lesson  1, 
although  his  scores  were  very  low.  Close  observation  of  the  boy  at  work 
showed  that  he  was  counting.  A  test  of  the  combinations  proved  that  he 
knew  them  verv  well.    A  little  experimental  testing  soon  discovered  the  fact 


TEACHER^S     MANUAL 39 

that  the  child's  trouble  came  wholly  on  the  second  addition.     In  the  example 
in  the  margin  the  11  was  given  instantly,  but  the  child  was  unable  5 

to  add  the  5  to  the  11  held  in  mind.    Nor  could  he  count  very  rapidly.  4, 

The  suggestion  was  made  that  he  picture  the  11,  as  written  on  the  7 

paper  underneath  the  5  in  position  for  adding.     This  he  was  able  " 

to  do  readily,  and  after  a  very  little  practice  showed  a  good  gain  in  his  scores. 
The  child  probably  had  a  strong  tendency  to  depend  upon  visual  imagery. 

The  practice  tests  will  readily  select  the  children  in  need  of  such 
special  assistance,  but  this  in  itself  is  of  little  value.  The  critical  factor  is  the 
skill  of  the  teacher  to  diagnose  conditions  and  to  prescribe  remedies.  How- 
ever, do  not  be  discouraged  if  you  have  had  no  experience  in  such  work. 
Very  few  teachers  have.  The  important  thing  is  a  willingness  to  try  and 
the  power  to  profit  by  your  experiences  and  by  your  mistakes. 

Lesson  2.     Subject,  Subtraction 

Borrowing 

Subtraction  is  the  easiest  of  the  four  processes.     There  is  very 
little  more  to  it  than  knowledge  of  the  combinations,  and  the  process 
of  borrowing.     The   correlation   between  the  combinations  and  the   .        21 
operation  itself  is  much  higher  than  in  addition.     The  combinations  9 

will  be  found  in  Lesson  46.  When  a  child  has  low  scores  in  Lesson 
2,  test  him  on  the  combinations.  Make  very  sure  he  knows  those 
with   a   minuend   larger   than   ten. 

Teaching  borrowing  is  merely  teaching  the  habit  of  seeing  a  num- 
ber as  1  and  the  next  lower  digit.    Thus,  in  the  example  shown  in  the  63, 
margin,   show  the  child  that  it  might  be  written  as  in  the  second  7 
form.     The  1  is  used  with  the  three  and  the  five  is  brought  down.           ' 

4  7 

Practice  the  child  in  seeing  5  as  ^^    8  as    -j^*  etc.,  then  teach  him  to 

link  the  1  to- the  figure  at  the  right.    The  one  remaining  point  is  dis-  ^3 

crimination  between  the  situation  where  borrowing  is  needed,  and 
where  it  is  not.  Do  the  first  work  with  the  single  combinations,  and 
then  with  Lesson  2. 


50 

1. 

7 


Do  not  trouble  the  child  with  explanations  about  the  place  value  of  the 
1  that  is  borrowed.  Do  not  expect  him  to  realize  that  it  is  really  a  "ten." 
Teach  children  to  borrow  by  imitation,  just  as  you  would  teach  them  to  use 
a  spoon  or  to  shoot  a  bow  and  arrow.  A  few  children  will  refuse  to 
imitate  until  they  understand  the  reason  for  the  actions,  and  in  such  cases 
the  reasons  should  be  given.  But  for  most  children  the  time  for  such 
explanations  is  when  skill  has  been  fully  developed.     In  particular  avoid  the 

y.  "seven  from  three  I  cannot  take.     Therefore.  I  borrow-"  etc.     Do  not 


I 


30 STANDARD     PRACTICE    TESTS 

allow  the  children  to  say  "seven  from  three."  As  with  the  addition  com- 
binations, they  should  read  the  remainders  without  saying  or  thinking  the 
subtrahend  or  minuend.  Many  children  in  the  upper  grades  are  unable  to 
subtract  without  repeating  the  whole  formula  learned  in  the  primary  grade. 

For  the  child  who  does  not  readily  get  the  "remainder"  idea,  try  the 
"completion"  idea    (Austrian  subtraction).     For  instance,  instead  of  saying 
"seven  from  thirteen,"  one  can  just  as  well  think  "seven  and  how  many  are 
thirteen."     Both  of  these  are  to  give  place   immediately  to   the 
mere  response  to  the  subtraction  situation,  "6."     In  Austrian  sub-  §3 

traction,  in  the  example  in  the  margin,  said  out  in  full,  seven  and  7 

how  many  are  13,  the  child  thinks  next,  one  and  how  many  are  "7^ 

six.     That  is,  the  one  from  the  thirteen  is  carried  as  in  addition. 
That  is  one  of  the  great  merits  of  the  Austrian  subtraction.     It 
has,  however,  nothing  like  the  superiority  which  its  advocates  claim  for  it, 
but  is  of  value  as  an  alternative  method  for  certain  children. 

Some  teachers  may  object  that  the  discussions  above  deal  wholly  with 
the  mechanical  phases  of  the  development  of  skill.  This  is  true.  Under- 
standing and  skill  are  two  separate  phases  of  training  which  have  no 
necessary  connection  with  each  other.  The  motive  for  subtraction  must 
come  from  real  situations  within  the  child's  experience,  and  the  discussion 
above  takes  it  for  granted  that  the  child  in  whom  the  skill  is  to  be  developed 
has  already  had  the  necessary  experiments  with  concrete  situations  demanding 
subtraction  to  develop  understanding  of  what  subtraction  is  and  why  the 
process  is  necessary.  The  one  mechanical  element  possibly  connecting  the 
two  is  the  appreciation  of  the  remainder.  The  child  who  subtracts  7  from 
63  should  realize  that  the  5  and  6  make  fifty-six.  If  he  is  unable  to  perceive 
them  as  a  single  number,  have  him  write  the  numbers  from  fifty  to  seventy 
in  a  single  column.  Have  him  point  to  sixty-three,  then  to  the  seventh 
number  below  it.  Work  in  this  way  until  the  child  develops  a  proper 
number  sense. 

Lessons  9,  17,  24,  33,  37,  and  41  also  deal  with  subtraction  but  present  no 
new  difficulties  and  will  not  be  referred  to  again.  They  simply  give 
practice  in  subtraction  with  larger  and  larger  numbers. 

Lesson  3.     Subject,  Short  Multiplication 

Without  Carrying 

In  multiplication,  as  in  addition,  there  is  little  correlation  be- 
tween knowledge  of  the  combinations  (or  tables)  and  the  ability  to  31 
multiply.  The  combinations  given  in  Lesson  47  should  not  be  __2 
studied  as  such,  although  the  tests'  are  convenient  in  locating 
difficulty  with  particular  combinations.  As  in  addition,  so  in 
multiplication,  do  not  let  the  child  say  "two  times  one,  two  times 
three."    He  knows  he  wants  to  multiply,  and  the  2  and  the  1  are  both  on  the 


TEACHER^S     MANUAL 31 

paper  and  present  to  his  mind  through  visual  stimuli.    The  re- 
sponse is  all  that  should  be  given.     Thus,  in  drill  on  combina- 
tions the  child  should  say  or  think  only  28,  24,  45.     So  in  mul-  T     c     k 
tiplying  31  by  2  the  child  should  think  and  write  only  2,  6  and          —   —    — 
read  62,  omitting  all  other  responses. 

As  in  addition,  the  most  efficient  way  to  learn  the  combinations  is 
repeated  practice  on  the  examples  in  Lesson  3.  If  a  child  does  not  know 
the  result  of  a  given  combination,  tell  him,  then  h^ve  him  practice  the 
example  over  and  over  until  it  is  remembered  readily,  even  if  the  same 
example  has  to  be  tried  once  or  twice  a  day  for  a  week  or  more.. 

Lesson  4.     Subject,  Short  Division 

Without  Carrying 

In  division,  as  in  subtraction,  the  correlation  between  the 
fundamental  facts  and  the  resulting  operation  is  much  higher 
than  for  addition  and  multiplication.     The  combinations  and  4)284 

tests  will  be  found  in  Lesson  48.     Be  sure  that  the  child  who 
has  had  trouble  with  Lesson  4  has  at  least  a  fair  command 
of  the  combinations,  then  let  him  practice  on  the  examples  of  Lesson  4.     In 
these  simple  divisions  there  is  no  need  of  "four  into  28,"  etc.     It  is  possible 
to  give  the  response  only  as  in  the  previous  lessons. 

Lesson  5.     Subject,  Addition 

Bridging  the  Tens 

Many  a  child  who  knows  his  combinations  perfectly  can- 
not succeed  in  column  addition,  because  for  all  sums  above  18  3g  +7  = 
he  must  count.    In  this  test  make  plain  to  the  children  that  the 
lesson  is  preparation  for  column  addition   (Lesson  8),  and  if 
the  children  add  the  7  to  the  8,  and  then  carry  one  to  the  three,  they  are  miss- 
ing the  benefit  of  the  lesson.   The  child  should  see  the  38  and  the  7  and  think 
of  45  only.    If  he  must  say  anything,  it  should  be  38,  7,  45. 

Many  children  have  difficulty  in  bridging  the  tens.  The  fault  is  usually 
with  the  concept  of  the  number  of  sequence.    Counting  by  tens  is  sometimes 


32 


STANDARD     PRACTICE    TESTS 


a  help.     Writing  the   numbers  down   in  order   and   moving  the  hand   as   in 


47 
46 
45 
44 
43 
42 
41 
40 
39 
38 
37 


is  worth  trying.  Still  an- 
other device  in  common  use 
is  the  adding  of  a  given 
digit  to  a  column  of  figures 
each  of  which  ends  in  a 
given  digit.  For  instance, 
for  practice  on  the  8-|-7 
combination  three  columns 
would  be  used  as  follows: 


A 

B 

C 

98 

8 

27 

88 

78 

58 

78 

58 

72 

68 

28 

63 

58 

68 

88 

48 

88 

45 

38 

98 

26 

28 

18 

18 

18 

38 

37 

8 

48 

91 

7  would  be 
added  to 
each  num- 
ber in  turn. 


Children  with  poor  memories  should  emphasize  the  tens,  as  thirty-eight 
instead  of  the  conventional  thirty-eight.  After  the  idea  of  bridging  the 
tens  is  once  established,  practice  soon  does  the  rest. 


Lesson  6.     Subject,  Multiplication 


Carrying 


To  establish  the  idea  of  carrying,  let  the  child 
write  at  first  both  partial  products,  as  shown  in  the 
margin,  so  that  he  can  see  the  way  the  number  car- 
ried is  added  to  the  next  partial  product.  Then  have 
him  practice  the  same  example  over  and  over,  do- 
ing the  carrying  mentally  until  the  w^ork  goes 
smoothly.  Then  have  him  try  another  example 
and  a  third,  until  sure  the  idea  is  established.    Practice  will  do  the  rest. 


32 
5 


32 

5 
10 
15 
160 


TEACHER^S     MANUAL 33 

Be  sure  the  children  have  the  right  habits  of  work.  In  multiplying  32 
by  5  the  child  should  say  or  think  only  10,  writing  the  zero,  then  15-16, 
writing  the  16.  If  the  child  has  difficulty  in  omitting  the  unnecessary  words, 
let  him  practice  on  very  easy  examples,  as  32,  23,  42,  24,  etc.,  making  use 
of  the  same  combinations  over  and  over  again.  Difficulty  in  omitting  un- 
necessary words  usually  means  lack  of  practice  on  Lesson  3. 

Lesson  7.     Subject,  Division 

Carrying 

The  first  point  of  difficulty  in  examples  of  this  type  is  the 
recognition  of  the  quotient  when  the  dividend  is  not  an  even  


multiple  of  the  divisor.     Let  the  child  write 


3x4=12)  3)138 


C  3  X  4=12  I 
I  3  X  5=15  j 


then  fill  in  the  13  and  14  between  12  and  15.    Under  ques- 
tioning he  will  be  able  to  work  out  3)13=^4  and  1  over,  3)14=  4  and  2  over. 
If  this  does  not  help,  have  him  make  out  for  different  divisors  a.  list  of 
dividends  like  the  following: 

3-f-3=l 

4r-^-3=l  and  1  over 

5-f-3=l  and  2  over 

6-f-3=2 

7  etc. 

The  second  difficulty  is  the  holding  in  mind  of  the  product  while  the 
subtraction  is  made.  Help  the  child  to  work  the  example  out  in  full  as  in 
long  division,  so  that  he  may  see  each  step  of  the  process,  then  have  him 
perfect  the  short  division  habit  by  much  practice  on  a  few  examples  before 
attempting  to  use  it  generally. 

In  division,  as  in  multiplication,  omit  unnecessary  words.  Most  chil- 
dren, however,  will  require  an  extra  step  as  follows:  In  working  3)138 
they  will  say  or  think  4-12-1-18-6,  although  many  are  able  to  reduce  this 
to  simply  4-18-6. 

Such  efficient  habits  increase  speed,  decrease  mental  strain,  and  are 
much  to  be  desired. 


34 STANDARD     PRACTICE     TE  S  T  S 

Lesson  8.    Subject,  Addition 

Process,  Column  Addition 

Column  addition  is  a  complex  habit  in  which  a  number  of 
elements  enter.  This  lesson  combines  and  extends  the  abilities 
developed  by  Lessons  1  and  5.     The  child  should  say  9,  10,  15,  3 

19,  25,  28  in  one  breath  smoothly,   without  break.    The  problem  6 

here  is,  not  addition,  but  the  reading  of  the  partial  sums.     Just  4 

as  pronouncing  words  is  not  reading,  so  merely  announcing  the  5 

various  partial   sums   one  after  another  is   not  column   addition.  1 

In  working  with  individuals,  do  not  be  content  with  correct  an-  7 

swers.     Put   before  the   child  smooth,   continuous  adding   as  the  2 

goal.     Here  again,   practice   on   first  one,   then   two,   then   small  ' 

groups  of  examples  will  enable  a  child  finally  to  finish  the  whole 
lesson  easily  within  his  time  allowance.  Speed  and  accuracy  without  strain 
are  therefore  the  test  as  to  whether  the  child  is  adding  in  the  proper  manner. 
This  is  one  of  the  important  lessons.  The  child  will  soon  begin  to  see 
the  sums  in  groups  as  9,  19,  28  or  10,  19,  28.  Do  not  force  this,  but  praise 
it  highly  when  it  occurs,  providing  only  it  does  not  involve  skipping  about  in 
the  columns.  The  grouping  must  not  interfere  with  the  onward  progress 
of  the  addition.    Any  habit  that  does  is  vicious. 

A  child  may  fail  in  this  lesson  because  he  has   a  very   short  attention 
span.     The  symptoms  and  remedy  for  this  trouble  are  given  in  Lesson  20. 

Lesson  9.    Subject,  Subtraction 

See  Lesson  2. 

Lesson  10.    Subject,  Long  Multiplication 

Process  Without  Carrying 

The  examples  in  this  lesson  call  for  no  carrying,  so  that  a 
child's  whole  attention  may  be  given  to  the  process.  The  new 
points  in  the  lesson  are  the  placing  of  the  partial  products  and  the  21 

addition  to  obtain  the  final  product.    Teach  these  by  the  imita'lion  13 

method,  showing  the  child  what  to  do,  but  not  by  telling  him  why  63 

it  is  done.    It  is  in  the  upper  grades  that  the  explanation  should  21 

be  discussed.     The  child  who  had  trouble  with  Lesson  1  is  quite  273 

likely  to  fail  here.     Remedy:  Review  Lesson  1  just  before  trying 
Lesson  10. 


TEACHER'S     MANUAL 35 

Lesson  11.     Subject,  Long  Division 

The  examples  in  this  lesson  call  for  no  carrying.     See  that 

the  child  gets  the  steps  of  the  process  well  established:  divide,  14 
multiply,  subtract,  bring  down.     In  every  example,  if  the  first            21)294 

figure  of  the  divisor  is  used  as  a  trial  divisor  the  quotient  will  be  21 

the  true  quotient.     Therefore,  teach  here  the  use  of  the  first  "m 

figure   of   the   divisor   as    a    trial   divisor.      (See   Lesson    19.)  g^ 

Teach  also  two  checks  which  should  always  be  applied  before  — 
and  after  subtraction:    Is  the  product  larger  than  the  partial 
dividend?     Is  the  remainder  larger  than  the  divisor? 

To  aid  the  child  in  discriminating  between  the  dififerent  cases,  prepare 
a  number  of  examples  incorrectly  worked,  and  have  him  tell  what  is  the 
matter  with  each. 

Illustrations 

4       Product    larger    than  divi-                2  Remainder   larger    than   di- 

62)1984    dend,    indicating   that  cor-  62)1984  visor,  indicating  that  corre- 

248       responding     digit     in  quo-            124  sponding   digit   in   quotient 

tient  is  too  large.  74  is  too  small. 

Be  sure  to  teach  that  in  such  cases  the  work  must  be  begun  over  again. 
Two  very  common  mistakes  by  children  are  subtraction  when  the  product 
is  too  large,  and  continued  division  without  bringing  dov/n  a  new  figure 
when  the  product  is  too  small. 


74,  the  remainder,  is  larger 
than  62,  so  the  child  has 
divided  again.  Proof  by 
multiplication  and  a  dis- 
cussion of  place  value  will 
remedy  the  trouble. 

For  very  dull  pupils,  teach  long  division  by  using  single  digits  for 
divisors. 

Work  for  the  omission  of  all  unnecessary  words'.  For  those  who  have 
learned  the  Austrian  subtraction,  the  process  of  division  can  be  greatly  sim- 
plified. This  is  the  real  advantage  of  the  method,  and  the  writer  believes 
that  all  should  learn  Austrian  division,  whether  they  learn  the  addition  or  not. 
The  actual   work  on  the   division   example   shown   in   the   margin   woul'd   Le 


Illustrations 

48 

212 

62)  1984 

248  is  subtracted 

62)1984 

248 

from  198 

124 

504 

74 

496 

62 

8 

124 
124 

36  S  T  A  NDARD     PRACTTCE    TESTS 

as  follows:  the  child  would  see  6)19  and  write  the  3,  would 
see  3  X  2  and  think  6  under  the  8,  then  two  more  would 
make  the  6  into  8,  so  that  he  would  write  the  remainder  2.  32 

The  rest  of  the  work  is  18-1-124-2-0-0.     That  is,  only  the  62)1984 

remainders   are  written,   the  multiplication  and   subtraction  124 

being  carried  on   mentally.     The  Austrian   method  of  bor- 
rowing (carrying)  makes  this  possible.    The  advantages  are 
that  it   saves   much   work  and  time;   the   disadvantages,    from   the   point   of 
view  of  the  teacher,  are  that  mistakes  are  harder  to  locate  since  more  of  the 
work  is  done  mentally. 

Lesson  12.    Subject,  Addition 

Carrying 

In  the  first  examples  in  this  lesson  the  sum  of  each  col- 
umn falls  in  the  tens,  so  that  the  number  to  be  carried  is  1.  9  5  6  6  8 
In  the  second  part  the  sums  are  all  in  the  twenties,  and  in             3  4  2  3  2 
the  last  part  the  sums  are  sometimes  one  and  sometimes  the  6  4  7  5  6 
other. 

In  adding  the  example  in  the  illustration,  a  child  should 
think  8,  16,  writing  the  6,  then  6  (5+1),  9,  15,  or  better  6, 
15,  or  10,  15.  That  is,  the  number  to  bQ  carried  should  be  added  to  the  first 
addend.  A  surprising  number  of  children  wait  until  the  addition  of  the  next 
column  is  completed  before  adding  the  number  carried.  Children^  with  weak 
memories  may  have  to  write  the  number  carried  at  the  top  of  the  next  column, 
but  this  should  not  be"  permitted  except  as  a  last  resort.  All  such  devices 
take  time  and  alter  the  original  example  so  that  checking  is  difficult. 

Lesson  13.    Subject,  Test  A 

The  child  has  now  completed  the  main  elements  of  the  four  processes', 
and  his  scores  in  Lesson  13  should  be  compared  with  his  previous  scores 
to  see  his  gain.  Some  of  the  children,  in  spite  of  apparent  good  work,  will 
show  no  gain  or  even  loss.  In  such  cases  suspect  either  cheating  (see  page 
20)  or  nervousness  that  may  arise  from  knowing  that  the  past  work  is 
being  tested.  In  the  latter  case  repeat  the  test,  using  first  Form  A  and  then 
Form  B,  until  the  nervousness  wears  ofif.  There  may  also  be  one  or  two 
cases  of  legitimate  lack  of  transfer.  These  will  repay  careful  study.  Very 
little  is  known  about  the  conditions  which  prevent  transfer  and  the  writer 
will  welcome  reports  of  the  experiments  of  others,  particularly  if  causes 
and  remedies  are  discovered. 

The  writer  advises  that  each  child  be  allowed  to  take  Lesson  13  as  he 
reaches  it  in  regular  order.  He  also  advises  that  Lesson  13  be  given  to  the 
entire  class  (including  those  excused  and  those  who  have  not  yet  reached  it) 
thirty-six  days  after  the  first  test.     Six  days  should  be  taken  for  the  work, 


TEACHER\S     MANUAL 37 

giving  first  Form  A  and  then  Form  B,  Lesson  13,  then  Lessons  30,  31,  both 
Form  A  and  Form  B,  in  order  to  determine  those  who  did  not  need  the  next 
group  of  drill  lessons.  (See  page  6.)  At  this  time  75%  or  more  of  the 
class  should  complete  Test  A  successfully. 

Be  sure  to  record  the  results  from  these  general  tests  in  the  summary  on 
page  47. 

Lesson  14.    Subject,  Multiplication 

The  Zero  Difficulties 

Many    children    develop    difficul- 
ties in  handling  zeros   in  multiplica-  cor\  n  i    e 
tion    and    division    examples.     Four            ^^^           *^3  ^^^  231 
cases  for  multiplication  are  given  in              ^^                ^^           ^^           ^^^ 
this  lesson.     Say  nothing  about  such         12600      21090        630           693 
difficulties  unless  the  child  makes  such                                            420         231 
mistakes.     Then  deal  with  each  child                                            4830"     2379*^ 
individually  and  show  the  analogy  be- 
tween the  handling  of  zeros  and  the 
handling  of  the  other  figures. 

When  ciphers  occur  at  the  end  of  numbers,  have  the  children  simply 
annex  the  proper  number  of  ciphers  to  the  product  of  the  significant  figures. 
Note  that  in  some  of  the  examples  where  a  zero  occurs  in  the  multiplicand, 
carrying  is  called  for.  This  is  a  new  point,  but  should  make  little  trouble 
after  Lesson  12.  When  the  zero  occurs  in  the  multiplier,  there  should  not 
be  three  partial  products,  but  two  only.  The  zero  means  that  there  is  no  mul- 
tiplier in  the  place  where  it  occurs.  The  child  may  write  one  zero  in  the 
product  to  hold  the  place,  if  he  must,  but  the  form  given  in  the  illustration 
is  better. 

Lesson  15.     Subject,  Division 

Zero  Difficulties,  Without  Carrying 

This  lesson  is  the  converse  of 
Lesson  14.  The  zero  difficulties 
are  a  frequent  source  of  inac-  690  510  302 


curacy,  particularly  the  third 
form  in  the  illustration.  When 
it  is  needed,  proof  by  multipli- 


71)48990    3)1530    31)9362 
426  93 


cation  is  often  a  good  way  of  639       \  62 

showing  a  child  the  reasons  for  ^39  o2 


the  methods  used.  31  x  32  will 
not  yield  9362,  while  31  x  302 
will. 


38  STANDARD     PRACTICE    TESTS 

Lesson  16.     Subject,  Addition 

Review  and  Combination.    Column  Addition  and  Carrying 

See  Lessons  8  and  12. 

Lesson  17*     Subject,  Subtraction 

See  Lesson  2. 

Lesson  18.     Subject,  Long  Multiplication 

With  Carrying 

582 
37 

Omitting  unnecessary  words  will  make  for  ease  and  4074 

accuracy  of  carrying,  as  the  number  to  be  carried  does  not  1746 

need  to  bfe  held  in  mind  for  so  long  a  time.  21*5^4 

Lesson  19.     Subject,  Long  Division 

With  Carrying 
The  examples  in  this  lesson  are  all  the  simplest  case  72 

in  long  division  with  carrying.     The  first  figure  of  the      63)4536 
divisor  is  the  trial  divisor,  and  the  trial  quotient  is  the  44^ 

true  quotient.  Make  the  point  that  the  child  does  not 
know  the  "63"  combinations;  that  it  would  be  easier  to 
divide  by  60,  the  nearest  round  number,  and  that  by 
dividing  by  60  with  the  zero  canceled  is  the  same  as 
dividing  by  6.  All  of  this  is  direct  preparation  for  later 
lessons  dealing  with  the  more  difficult  cases. 

Lesson  20.     Subject,  Addition 

Attention  Span 

Many  children  who  have  no  trouble  with  Lesson  8  will  fail 

on  this  lesson  and  have  many  answers  wrong.    The  reason  is  a  9 

psychological  and  not  an  arithmetical  one.     The  human  mind  2 

is  so  constructed  that   it   is  difficult  for  it  to  give  continuous  4 

attention  to  any  stimulus  for  a  long  interval.    There  are  waves  8 

or  pulses  in  one's  attention,   and  when  the  attention  is  at  a  2 

low  phase,  the   mind  is  very  likely  to  be  diverted  by  sights,  7 

sounds,   or  thoughts    of    a    different    character.     Experiment  5 

shows  that  most  children  can   add   steadily   for  six  additions.  3 

In  the  illustration  this  would  mean  that  a  well-trained  child  6 

would  be  able  to  say  16,  20,  21,  27  easily  and  smoothly,  that  1 

30  and  35  would  come  a  little  less  readily,  and  that  the  child  4 

would  apparently  stick  on  35-|-7,  going  over  and  over  it  with-  8 

out   being   able   to   name   the   sum.     If  the   column  had   been  8 

added  16,  21,  30,  42,  52,  56,  the  apparent  difficulty  would  be  — 
to  add  56  and  2. 


126 
126 


TEACHER^S     MANUAL 39 

The  difficulty  is  in  the  mind,  however,  and  not  in  the  combinations. 
The  adding  activity  seems  to  give  rise  to  nerve  currents  v^hich  have  no 
habitual  path  of  discharge,  and  so  are  dammed  up,  as  it  were,  by  the 
adding  activity  until  the  time  comes  when  they  are  strong  enough  to  throw 
the  entire  adding  mechanism  out  of  gear.  They  are  then  released  and  dis- 
charged along  some  nerve  path  in  the  body,  causing  involuntary  movements, 
as  sighs,  frowns,  etc.,  or  altering  the  tension  of  certain  muscles  or  the 
activity  of  certain  internal  organs,  etc.,  etc.  As  a  person  has  more  and 
more  practice  in  addition  he  learns  to  do  two  things:  (1)  to  hold  firmly 
in  mind  the  last  partial  sum  during  the  period  of  disturbance;  and  (2)  con- 
sciously to  interrupt  the  adding  activity  and  give  the  confusion  currents  a 
chance  to  discharge.  The  writer,  for  instance,  repeats  the  sum  to  be  re- 
membered, as  "35,  35,  35,"  and  at  the  same  time  consciously  moves  his 
eyes  away  from  the  column  being  added,  simultaneously  taking  a  long 
breath.  He  is  then  ready  to  continue  the  adding  actively  for  another 
interval. 

The  degree  of  difficulty  caused  by  such  confusion  currents  varies 
enormously  in  different  people.  Some  show  no  signs  of  it  whatever.  Some 
have  an  attention  span  of  but  three  or  four  additions.  There  is  evidence 
tending  to  show  that  the  average  span  is  about  six  or  eight  additions. 
These  are  the  cases  that  usually  make  difficulty.  Lesson  20,  therefore,  with 
columns  twelve  additions  long,  should  bring  all  such  trouble  to  light.  It  will 
also  serve  to  detect  children  having  a  span  several  examples  long.  For 
instance,  if  a  child  misses  approximately  every  fourth  or  fifth  example, 
suspect  the  same  difficulty,  but  a  long  span. 

The  difficulty  is  easily  recognized  by  its  symptoms.  If  the  child  hesi- 
tates at  regular  intervals  in  a  column,  if  he  goes  over  and  over  a  given 
addition  and  is  apparently  unable  to  think  at  all,  if  he  gives  up  in  the  middle 
of  a  column  and  begins  again,  the  difficulty  is  almost  sure  to  be  one  of  this 
nature. 

The  remedy  is  obvious.  Teach  the  child  to  recognize  the  difficulty 
when  it  occurs,  to  avert  his  attention  momentarily  by  lifting  his  eyes  and 
taking  a  deep  breath,  to  keep  his  place  in  the  column  by  pointing  with  his 
pencil,  and  to  remember  correctly  the  partial  sum.  Children  are  apt  to  get 
entangled  in  the  situation,  and  to  go  over  helplessly  the  same  addition  so 
"long,  that  when  the  crisis  occurs  and  the  mind  clears,  the  additions 
which  had  been  made  previously  are  totally  forgotten. 

Lesson  21.     Subject,  Multiplication 

Merely  Longer  Examples  for  Further  Practice 


40  STANDARD     PRACTICE    TESTS 


Lesson  22.     Subject,  Division 

Second  Case 

This  lesson  covers  the  second  case,  where  the  trial 
divisor  is     one  larger    than  the    first  figure     of  the  di- 
visor, but  the  trial  quotient  is  the  true  quotient.  50 
A   child    without   much    imagination    or   number  49 
^^              sense   will   have   difficulty   in   recognizing   50   as  48 
the    nearest    round    number    to    49.     Have    such  47 


49)3087 

294  ^  child  actually  write   out   on  paper   the   whole         46 

of  the  tens  in  which  the  divisor  falls,  as  shown  45 

in  the  illustration.     He  can  then  see  that  49  is  44 

nearer   to   fifty  than   forty   and   appreciate  that  43 

when  the  second  figure  of  the  divisor  is  larger  42 

than   five,   he  must   use,   not   the   first  figure  of  41 

the    divisor,    but   the    next    larger    digit    as    the  40 

trial  divisor.  If  much  practice  in  finding  the  nearest  number  does  not  help, 
have  the  child  multiply  63  by  each  of  the  numbers  from  40  to  60  and  divide 
each  product  by  the  multiplier  from  which  it  came.  If  the  child  uses  the 
first  figure  of  the  divisor  as  the  trial  divisor  in  all  these  cases,  he  will  make 
mistakes  in  four  or  five  cases.  That  is,  his  first  trial  quotient  will  not  be 
the  true  quotient.  The  teacher  must  remember  that  the  use  of  a  trial  divisor 
was  originally  the  result  of  much  experience,  and  the  child  without  either 
experience  or  imagination  will  not  appreciate  readily  the  value  of  a  device 
which  eliminates  many  mistakes.  The  result  will  be  a  slow  speed  and  the 
irritation  which  comes  from  making  errors.  Successful  use  of  the  proper 
trial  divisor  can  easily  be  shown  to  "pay." 

Lesson  23.     Subject,  Addition 

Combination  of  Attention  Span  and  Carrying 

See  Lessons  19  and  20. 

Lesson  24.     Subject,  Subtraction 

See  Lesson  2. 

Lesson  25.     Subject,  Multiplication 

Practice  with  Longer  Examples 


TEACHER^S     MANUAL. 41 

Lesson  26.     Subject,  Division 

Third   Case,   Where  the  First   Figure  of  the   Divisor   Is  the  Trial 

(Divisor,  but  the  True  Quotient  Is  One  Smaller  than  the 
Trial  Quotient 
The  teacher's  task  here  is  to  develop  caution  and  judgment 
n  the  child.     In  this  lesson,  the  method  previously  followed  89 

)roduces   incorrect  results.     The  beginner  is   apt  to   feel  that        63)5607 
the  selection   of  the  true  quotient  is  only  guesswork,   but  the  504 

teacher  must  lead  him  to  see  that  the  mere  determination  of  "567 

a  trial  quotient  is  not  enough,  that  he  must  not  proceed  with  567 

the  work  of  division  until  he  has  estimated  at  least  the  probable  ■"-" 

effect  of  the   second   figure   in  the   divisor   upon  the  product. 
Gradually  he  will  come  to  see  that  when  the  dividend  is  al- 
most an  exact  multiple  of  the  first  figure  of  the  divisor,   the 
true  quotient  will  probably  be  one  less  than  the  trial  quotient.     In   a  large 
number  of  such  cases  he  will  get  the  true  quotient  on  the  first  trial,  and  the 
greater  the  number  of  successes  the  better  his  judgment.     He  will  also  be 
learning  another  lesson  of  great  value,  that  there   are  situations  in   life  in 
which  it  pays  not  to  go  ahead  until  the  consequences  of  an  action  have  been 
carefully  determined. 

Lesson  27.    Subject,  Addition 

Practice  with  Larger  Examples 

Unfortunately,  when  the  number  of  examples  is  so  few,  the  answers 
are  soon  learned.  Have  the  child  make  up  his  own  examples  for  practice, 
and  alternate  Form  A  and  Form  B   for  tests. 

Lesson  28.     Subject,  Multiplication 

Practice  with  Larger  Examples 

Lesson  29.    Subject,  Division 

The  Fourth  Case,  Where  the  First  Figure  of  the  Divisor  Must  Be 

Increased  by  One  to  Obtain  a  Trial  Divisor,  and  the  Second 

Trial  Quotient  Must  Be  Increased  by  One  to  Get 

the  True  Quotient 

79 
This  case  is,  of  course,  very  much  like  the  last   (Lesson        3g\2844 
26),  except  that  the  difficulty  comes  in  the  second  figure  of  the  252 

quotient  instead  of  the  first.     Judgment  must  be  built  up  slowly  "ooj. 

in   the   same   way   as  before.  qoa 


42 STANDARD     PRACTICE    TESTS 

Lessons  30,  31.    Subject,  Test  B 

These  two  lessons  form  a  single  test,  and  only  the  children  who  are 
perfect  in  both  tests,  or  have  but  a  single  example  wrong  in  the  two  days' 
work,  should  be  excused  from  drill  on  Lessons  14-29.  The  score  in  Test  B 
is  the  sum  of  the  scores  for  Lessons  30  and  31,  not  either  score  alone. 

The  reason  for  the  two  tests  is  that  the  examples  are  so  long  that  only  a 
few  can  be  done  in  three  minutes.  In  a  single  test  covering  the  four  opera- 
tions, the  result  would  be  based  upon  so  few  examples  of  each  operation 
that  its  reliability  would  be  low.  Even  under  the  present  arrangement,  any 
child  excused  from  drill  because  of  success  in  this  test,  but  inaccurate  in 
daily  work  in  arithmetic,  should  be  put  back  into  the  drill  class. 

Test  B  should  be  given  again. as  a  general  test  48  days  after  the  first 
trial. 

Be  sure  to  compare  the  results  of  the  second  trial  of  this  test  with  the 
first,  and  to  record  the  same  in  the  summary,  on  page  47  of  the  Teacher's 
Manual.    Read  again  page  22. 

Following  the  second  trial  of  Test  B,  give  Test  C,  Lesson  44,  Forms 
A  and  B,  to  determine  the  children  who  should  be  excused  from  drill  on 
Lessons  32  to  43. 

Note  that  Test  C  measures  endurance  and  calls  for  double  the  usual 
time  allowance.  In  Grades  4,  5,  and  6  only  the  exceptional  child  will  reach 
the  last  group  of  lessons.  It  is  expected  that  about  75%  of  the  children 
will  finish  Lesson  31  in  a  half  year.  In  the  sixth,  seventh,  and  eighth 
grades,  therefore,  more  and  more  children  will  be  excused  from  the  earlier 
lessons,  so  that  eventually  75  or  80%  will  finish  all  the  lessons.  However, 
do  not  expect  this  the  first  year  the  tests  are  used.  If  30%  finish  all  the 
lessons  in  the  eighth  grade  the  first  year,  the  class  is  better  than  the  average. 

Lesson  32.    Subject,  Addition 

Addition  of  Numbers  of  Different  Lengths 

14896 
635 

Difficulties  in  this  lesson  are  likely  to  be   wholly  difficulties  74 

of  attention.     Make  sure  the  child  understands  that  he  is  to  add  380 

merely  the  figures  that  appear  in  any  one  column,  and  show  him  7492 

how  to  follow  up  a  column.    Practice  will  do  the  rest.  •  *6 

^  85 

294 
54957 


I 


TEACHER^S     MANUAL 43 

Lesson  33.    Subject,  Subtraction 

Practice  with  Long  Examples 

Lesson  34.     Subject,  Multiplication 

Practice  with  Long  Examples 

Lesson  35.    Subject,  Division 

Practice  with  Long  Examples 

Lessons  36,  37,  38,  39.    Subject,  Endurance 

These  examples  are  taken  from  the  writer's  Research  Tests,  Series  B, 
Forms  1  and  2,  and  are  the  smallest  examples  that  will  measure  all  the  com- 
ponent abilities  that  enter  into  each  operation.  They  also  measure  endur- 
ance. It  is  not  enough  that  a  child  be  able  to  figure  correctly  for  a  short 
interval.  He  must  be  able  to  keep  at  it  for  some  time.  The  time  interval 
is  accordingly  doubled,  and  the  confusion  of  scoring  papers,  etc.,  of  the 
children  who  have  not  reached  these  tests  is  an  added  factor  of  difficulty. 
In  business  offices  computations  must  be  carried  on  in  spite  of  noise,  con- 
fusion, and  interruption.  Help  the  child  to  get  the  necessary  poise  and 
concentration  in  the  busy  classroom.  Practice  is  the  only  remedy  needed 
for  failure. 

Forms  3  and  4  of  the  Research  Tests  Series  B^  are  composed  of  entirely 
different  examples  of  equal  value,  and  are  available  to  measure  the  results 
of  the  use  of  the  Practical  Tests,  or  for  other  research  work. 

Lessons  40,  41,  42,  43.     Subject,  Copying 

The  examples  in  these  lessons  are  based  upon  the  writer's  Research 
Tests,  Series  A,  Test  7.  Measurement  has  proved  the  very  great  need  for 
training  in  copying.  The  difficulties  that  arise,  so  far  as  is  known,  are  due 
wholly  to  lack  of  concentration  or  attention. 

Lesson  44.     Subject,  Test  C 

Allow  six  minutes  for  this  test. 

This  test  measures  endurance  and  copying  in  the  four  operations.  In 
almost  all  commercial  work  records  must  be  copied  from  slips  to  books,  and 
from  one  book  to  another.  Such  copying  calls  for  a  peculiar  kind  of  atten- 
tion, which  may  or  may  not  be  generated  by  the  previous  work.  Every 
answer  must  not  only  be  correct,  but  written  in  the  correct  space  in  the 
answer  column.  ' 


*  These  may  be  obtained  from  S.  A.  Courtis,  82  Eliot  St.,  Detroit,  Mich. 


44 STANDARD     PRACTICE    TESTS 

The  child  who  completes  Test  C  successfully  has  no  further  need  of 
drill  work,  except  the  incidental  drill  of  daily  use  of  computation  in  his 
arithmetic  work. 

As  with  previous  tests,  be  sure  to  keep  on  page  49  a  record  of  your 
results  on  both  the  first  and  second  trial  6f  this  test. 

Lessons  45,  46,  47,  48.    Subject,  Combinations  in  the 
Four  Operations 

For  use,  see  Lessons  1  to  4. 


Conclusion 

The  foregoing  lessons  have  been  designed  to  cover  every  known  diffi- 
culty in  the  development  of  ability  in  the  four  operations  with  whole  num- 
bers. Unfortunately,  the  collection  of  such  difficulties  has  been  a  recent 
activity,  and  the  author  will,  therefore,  welcome  letters  from  teachers  giving 
symptoms  and  remedies  for  difficulties  that  have  not  fallen  within  his  teach- 
ing experience,  that  the  series  of  lessons  may  be  made  more  complete.  For 
the  same  reason  he  will  welcome  results  of  tests,  and  summaries  of  the 
time  required  to  complete  the  different  groups  of  lessons,  etc.,  that  the  same 
may  be  completely  standardized. 


TEACHER'S  RECORD  SHEET 


Name. 


.School. 


Grade.. 


Name  of  Children 

Score 

Number  of  Trials  to  complete  successfully  Lesson 

Score 

! 

Test 
A 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

te.t 
A 

1                       •    I 

1 

2 

1 

3 

-- 

4 

5 

1 

\ 

O 

1 

7 

1 

1 

8 

1 

1 

1 

1 

0                                        1 

i 

1 

10                                    1 

1 

1 

1 

11                  1 

1       1       1 

1 

12                                          1 

1      1 

1 

13                                          1 

14                          ! 
ir>                           ■  1 

, 

1 

1 

t 

ir,                               i     ! 

1 

1 

17                                   f     1 

— 

1 

• 

18 
lO 
20 
21 
22 
23 
24 

1 

1 

1 

1 

1 

— 

1 

1      1      1 

1       1 

1       ! 

1      1      1 

1 

1       t 

1      1      1 

25                                        1      1 

1       1 

1      1      1      1      1 

2(5                                          1      1 

1       1 

III 

27 

1 

1       1 

i 

III 

28 

1 

1       1 

i 

1      1      1      1 

29 

1 

1       1 

-1      1      1      1 

30 

1      1 

Forward 

45 


TEACHER'S  RECORD  SHEET  (Continued) 


Name. 


Schools 


Grade. 


Name  of  Children 

Score 

Number  of  Trials  to  complete  successfully  Lesson 

Score 

Te.t 
A 

1 

2 

3 

4 

5 

6 

^ 

8 

9 

10 

11 

12 

te.t 
A 

31 

32 

1 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

1 

44 

45 

! 

46 

j 

47 

1 

48 

1 

j 

49 

50 

51 

52 

53 

1 

I 

54 

■ 

1 

r 

55 

!      1 

1 

56 

1 

1 

1 

57 

1     !     1 

i 

58 

— 

59 

— 

60 

Forward 

46 


I   TEACHER'S  RECORD  SHEET  (Continued) 


Name School. 


Grade. 


Name  of  Children 

"el 

Number  of  Trials  to  complete  snccetsfnlly  Lesson 

i 

feit 
B 

14 

16 

16 

17 

18 

19|20 

21 

22 

23 

24 

26 

26 

27 

28 

29 

tlTt 

B 

1 

1 

»> 

1 

;{ 

1 

4 

1 

5 

1 

6 

i 

.     1 

7 

1 

8 

1 

9 

j 

lO 

1 
1 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

' 

2.-» 

26 

27 

28 

29 

\ 

30 

Forward 

47 


TEACHER'S  RECORD  SHEET  (Continued) 


Name. 


.School Grade. 


Name  of  Children 

i 

Number  of  Trials  to  complete  snccessfnlly  Lesson 

1 

Test 
B 

14 

16 

16 

17 

18 

19|20|3122 

2324 

25 

2627 

2829 

Test 
B 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

— 

48 

49 

50 

51 

52 

53 

54 

55 

i 

1 

56 

57 

58 

59 

(JO 

Total 

48 


TEACHER'S  RECORD  SHEET  (Continued) 


SchooL 


....  Grade.. 


Name  of  Children 

Score 

Number  of  Trials  to  complete  successfully  Lesson 

Score 

Test 
C 

32 

33 

34 

35 

36 

37 

383940 

41 

42 

43 

test 
C 

1 

2 

- 

3 

1 

4 

5 

6 

7 

8 

9 

lo                           ! 

11 

12      . 

13 

14 

15 

- 

16 

17 

18                                         1 

19                                        1 

20                                        1 

1 

21 

1 

1 

22 

1 

23 

1 

1 

24 

! 

1 

25 

I 

1 

20 

27 

28 

29 

30 

! 

_. 

Forward 

49 


TEACHER'S  RECORD  SHEET  (Continued) 


Name.. 


School. 


Grade.. 


Name  of  Children 

Score 

Number  of  Trials  to  complete  snccessfnlly  Lesson 

Score 

Test 
C 

32 

3334363637 

38394041 

42 

43 

test 
C 

31 

32 

1 

33 

1 

34 

35 

36 

1 

37 

1      1 

38 

1 

39 

1 

1 

40 

1      1      1 

i 

41 

!     1     1 

1 

42 

1     - 

- 

1 

43 

1 

1 

44 

] 

45 

46 

1 

! 

47 

1 

1 

1 

48 

1     1     1 

1 

49 

j      i 

1 

50 

1      j 

] 

51 

1        1        1 

52 

1        1        1 

53 

1     1     1 

1        1 

64 

1     1     1     1  • 

1               i 

1      i 

BS 

1     1     !     1     1     i 

1 

56 

1    !    1    1    1    1 

1      1 

57 

{    j    1        1 

1      1 

58 

Mini 

1      1 

59 

1 1 1 1 1 

1      1 

60. 

1    M    1    1 

!    1 

Total 

1 

Report  of  Test 


Teacher. 


SchooL 


Grade. 


Room. 


Date- 


Form. 


1st  Trial     2d  Trial 


Total  number  of  children  in  class 


Number  having  perfect  papers. 


Per  cent  having  perfect  papers 


Number  missing  but  one  example. 


Per  cent  missing  but  one  example 


Number  excused  from  Lessons  Nos. 


Per  cent  excused  from  Lessons  Nos.. 


Efficiency. 


Efficiency  Previous  Trial. 


Gai 


am. 


51 


SUMMARY-TIME  COST 


Teacher 

To  be  filled  out  at  end  of  term 
School 



Grade 

Number  of  Days 

No. 
Lessons 
Finished 

Names 

1 

Tests 

.essons 

Practice 

Excused 

Omitted 
or  Absent 

Total 

1 

2 

8 

4 

5 

O 

1 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

- 

__- 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

1 

27 

28 

29 

30 

Forward 

52 


SUMMARY-TIME  COST  (Continued) 


Teacher. 


To  be  filled  out  at  end  of  term 
School 


Grade.. 


Number  of  Days 

No. 
Lessons 
Finished 

Names 

Tests 

Lessons 

Practice 

Excused 

Omitted 
or  Absent 

Total 

31 

32 

33 

~ 

34 

35 

36 

37 

• 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

63 

54 

55 

56 

57 

58 

59 

69 

1 

Totals 

• 
cent  of  time  sav 

^d 

(Divide  the  total  of  the  excused  column  by 
the  sum  of  the  totals  of  tests,  lessons,  prac- 
tice, and  excused  columns.) 

53 

54 STANDARD     PRACTICE    TESTS 

ANSWERS 
Lesson  No.  13  Test  A  Lessons  1-12 

Form  A 

Add  '  Subtraction 

96  50  68  71 

23  74  19  28 

41     36    37    42    25    35 

34  75  68  85 

Multiplication 
744         966        299        2982      1488      2397 


19  21  13 

Division 

37  82 


TEACHER'S     MANUAL 55 

ANSWERS 
Lesson  No.  13  Test  A  Lessons  1-12 

Form  B 

Add  Subtraction 

58  61  78  49 

16  94  33  84 

37     24     40     35     29     37 

47  96  50     /    47 

Multiplication 
399         672         559         1887       2788       2993 


24  23  23 

Division 

42  62 


56 STANDARD     PRACTICE     TESTS 

ANSWERS 
Lesson  No.  30  Test  B  Part  1  Lessons  14-29 


Addition 

Form  A 

4816  5767  6199 


Form  B 

6119  4866  5797 


Subtraction 


Form  A 

64879321       88225099      18115955 


FormB 

76884659       82657718       96538845 


TEACHER^S     MANUAL 57 

ANSWERS 

Lesson  No.  31  Test  B  Part  11  Lessons  14-29 

Multiply 


Form  A 

579014  585354 

FormB 

741228  416698 


Divide 


Fonn  A 

861  973 

Form  B 

971  862 


58  STANDARD     PRACTICE     TESTS 

ANSWERS 

Lesson  No.  44  Test  C  Lessons  32-43 

Form  B  Double  Time 


Form  A 

531813 

9776756 

5353488 

6987 


Form  B 

510157 
7676759 
75844608 
7897 


Contents 


Page 

Personal  Note  to  Teachers 2 

Ten  Essential  Points 3,  4 

Section  I 

General  Description 5 

Program    6 

Section  II 

Detailed  Instructions — 

Monday 7 

Tuesday    7-11 

Wednesday    11-13 

Thursday   13-16 

Friday   16 

Monday    16,  17 

Tuesday    17 

Wednesday,  Thursday,  Friday 17, 18 

Monday 18-20 

Section  III 

Diagnosis  and  Remedy  of  Individual  Defects — 

Cheating    20,  21 

Transfer   22 

Efficiency 22 

Types 23 

Age    23 

Temperament 23,  24 

Physical  Condition   24,  25 

Mental  Traits 25 

Speed    26 

Mental  Deficiency 26,  27 

Miscellaneous   27 

Practice  Lesson    1 27-29 

2 29,30 

3 30,31 

4 31 

5 31,32 

6 32,33 

7 33 

8 34 

9 34 

59 


60 


STANDARD     PRACTICE     TESTS 


Practice  Lesson  10 


Page 
34 


11 35,36 


12, 


36 


21. 
22. 
23. 

24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 
32. 
33. 
34. 
35. 
36. 
37. 
38. 
39: 
40. 
4.1. 
42. 
43. 
44. 
45. 
46. 
47. 
48. 


43, 


39 

40 

40 

40 

40 

41 

41 

41 

41 

42 

42 

42 

43! 

43 

43 

43 

43 

43 

43 

43 

4^ 

43 
44 
44' 
44 

44 
4^ 


Teacher's  Records — 

Daily  Record    45-50 

Report  of  Tests 51 

Summary    52,  5i 


I 


Index 


Addition  Lessons — 

Lessons 1,    5,    8,12,16,20,23,27,32,36,40 

Page 27,  31,  34,  36,  38,  38,  40,  41,  42,  43,  43 

Alternative   Methods    12 

Answers — 

Lessons    9 

Tests , 54-58 

Reading  of 9 

When  correct 9 

Attention  Span    38 

(Austrian — 

Division    35 

Subtraction 30 

Borrov^ing — subtraction    29 

Bridging  Tens   31 

Carrying — 

Addition    36 

Subtraction    29 

^            Multiplication    32 

X           Division 33 

Cases  in  Division — 

I    38 

II    40 

III   41 

IV 41 

Combinations — 

Addition    27 

Subtraction    29,  30 

Multiplication    30,  31 

Division   31 

Copying 43 

Correction  of  Lessons — 

Children    9 

Teacher    11 

Detailed  Instructions   7 

Diagnosis  of  Defects  20 

Difficulties 20 

61 


62 


Division — 
Lesso 
Pages 

Efficiency    .^ 
Elimination 


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1,  43,  43,  43 
23 


Forms  A  ar 

General  De 

Graphs — 

Drav 

Meat 

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Use 
Habits  of  ^^ 

Add 

Subl 

Mul 

Div; 

Home  Stu 
Illustratio 

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Immaturi 
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Judgmen 

In 

In 
Measure 

Memory 

Mental 
Mental 
Multipli 


-1^ 


9 


iVJAY    10  g^^ 


Lessons 


11 

5 
5 


LD  21-95m-7.'37  ;     28,   34,   38,   42 


Pa^e    30,  32,  34,  37,  38,  39,  40,  41,  43,  43,  43 

24 
Nervousness    

24 
Periods  of  Grov^th 


^ TEACHER^S     MANUAL 63 

Physical  Condition   24 

Practice  : 16,  38 

Precocious  Children   23 

Process. — 

Addition 27 

Subtraction    29 

Multiplication 30 

Division    31 

Program 6 

5  Records — 

f            Children  18 

Teachers    15,  45-50 

Eeliability  of  Results 10 

Reports  of  Tests • 51 

Elesearch  Tests 43 

Retarded  Children 23 

Sample  Records — 

Graphs    19 

wScoring — 

'  I  Children   , 10 

Speed , 26 

vSubtraction — 

Lesson    2,     9,  17,  24,  33,  37,  41 

Page 29,  34,  38,  40,  43,  43,  43 

Summary   52,  53 

Teacher's  Record — 

Scoring , 14,  15,  45-50 

liTeaching — 

Graphs    19 

How  to  Study 16 

^Temperament   23 

Tests  A : 6,  7-10,  36 

Tests  B 6,  12,  42 

Tests  C ....6,  12,  43 

Time  Allowances 9 

Transfer 22 

Types .;.,. ,,... 23 

Warnings :.*.;*. .  •  .  V :  .• 12 


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